Illustrative Math Alignment: Grade 7 Unit 7
Expressions, Equations, and Inequalities
Lesson 9: Dealing with Negative Numbers
Use the following Media4Math resources with this Illustrative Math lesson.
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Math Example: Solving Two-Step Equations: Example 21 | Math Example: Solving Two-Step Equations: Example 21TopicSolving Equations DescriptionThis math example demonstrates solving the equation 2x - (-3) = x + 4. The solution involves adding -3 to both sides and then subtracting x from both sides to isolate the variable. The final result is x = 1. This example showcases the process of solving a two-step equation with negative numbers. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations: Example 22 | Math Example: Solving Two-Step Equations: Example 22TopicSolving Equations DescriptionThis math example illustrates the process of solving the equation 2x - (-3) = x - 4. The solution involves adding -3 to both sides and then subtracting x from both sides to isolate the variable. The final result is x = -7. This example demonstrates how to handle negative numbers and subtraction in two-step equations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations: Example 23 | Math Example: Solving Two-Step Equations: Example 23TopicSolving Equations DescriptionThis math example demonstrates solving the equation 5x - (-7) = 18. The solution involves adding -7 to both sides and then dividing by 5 to isolate the variable x. The final result is x = 2 1/5 or 2.2. This example showcases how to handle negative numbers and fractions in two-step equations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations: Example 24 | Math Example: Solving Two-Step Equations: Example 24TopicSolving Equations DescriptionThis math example illustrates the process of solving the equation x/2 - (-4) = 8. The solution involves adding -4 to both sides and then multiplying by 2 to isolate the variable x. The final result is x = 8. This example demonstrates how to handle fractions and negative numbers in two-step equations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations: Example 25 | Math Example: Solving Two-Step Equations: Example 25TopicSolving Equations DescriptionThis math example demonstrates solving the equation 3(x + (-2)) = 12. The solution involves first dividing both sides by 3 to isolate the expression x + (-2), then adding 2 to both sides to isolate x. The final result is x = 6. This example showcases how to handle parentheses and negative numbers in two-step equations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations: Example 26 | Math Example: Solving Two-Step Equations: Example 26TopicSolving Equations DescriptionThis math example illustrates the process of solving the equation 3(x - (-2)) = 15. The solution involves first dividing both sides by 3 to isolate the expression x - (-2), then subtracting 2 from both sides to isolate x. The final result is x = 3. This example demonstrates how to handle parentheses and double negatives in two-step equations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations: Example 27 | Math Example: Solving Two-Step Equations: Example 27TopicSolving Equations DescriptionThis math example demonstrates solving the equation 14(-15x) = 280. The solution involves first dividing both sides by 14 to isolate the expression -15x, then dividing by -15 to isolate x. The final result is x = -1/3. This example showcases how to handle multiplication with negative numbers and fractions in two-step equations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations: Example 28 | Math Example: Solving Two-Step Equations: Example 28TopicSolving Equations DescriptionThis math example illustrates the process of solving the equation 12(x/-5) = 144. The solution involves first dividing both sides by 12 to isolate the expression x/-5, then multiplying by 5 to isolate x. The final result is x = -60. This example demonstrates how to handle fractions and multiplication in two-step equations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations: Example 29 | Math Example: Solving Two-Step Equations: Example 29TopicSolving Equations DescriptionThis math example demonstrates solving the equation (x + (-4)) / 5 = 12. The solution involves first multiplying both sides by 5 to isolate the expression x + (-4), then adding 4 to isolate x. The final result is x = 64. This example showcases how to handle fractions and negative numbers in two-step equations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations: Example 3 | Math Example: Solving Two-Step Equations: Example 3TopicSolving Equations DescriptionThis example demonstrates solving the equation 2x + 4 = 8. The solution process involves subtracting 4 from both sides of the equation, then dividing both sides by 2. Through these steps, we find that x = 2. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations: Example 30 | Math Example: Solving Two-Step Equations: Example 30TopicSolving Equations DescriptionThis math example illustrates the process of solving the equation (x - (-4)) / 5 = 12. The solution involves first multiplying both sides by 5 to isolate the expression x - (-4), then subtracting -4 to isolate x. The final result is x = 56. This example demonstrates how to handle fractions and double negatives in two-step equations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations: Example 31 | Math Example: Solving Two-Step Equations: Example 31TopicSolving Equations DescriptionThis math example demonstrates solving the equation (2/3)x = -50. The solution involves first multiplying both sides by 3 to eliminate the fraction, then dividing by 2 to isolate x. The final result is x = -75. This example showcases how to handle fractions and negative numbers in two-step equations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations: Example 32 | Math Example: Solving Two-Step Equations: Example 32TopicSolving Equations DescriptionThis math example illustrates the process of solving the equation x / (4/5) = -30. The solution involves first multiplying both sides by 5 to eliminate the fraction in the denominator, then dividing by 4 to isolate x. The final result is x = -600. This example demonstrates how to handle complex fractions and negative numbers in two-step equations. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations: Example 4 | Math Example: Solving Two-Step Equations: Example 4TopicSolving Equations DescriptionThis example demonstrates solving the equation x/2 + 4 = 8. The solution process involves subtracting 4 from both sides of the equation, then multiplying both sides by 2. Through these steps, we find that x = 8. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations: Example 5 | Math Example: Solving Two-Step Equations: Example 5TopicSolving Equations DescriptionThis example demonstrates solving the equation 2x - 3 = x + 4. The solution process involves adding 3 to both sides of the equation, then subtracting x from both sides to isolate the variable. Through these steps, we find that x = 7. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations: Example 6 | Math Example: Solving Two-Step Equations: Example 6TopicSolving Equations DescriptionThis example demonstrates solving the equation 2x - 3 = x - 4. The solution process involves adding 3 to both sides of the equation, then subtracting x from both sides to isolate the variable. Through these steps, we find that x = -1. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations: Example 7 | Math Example: Solving Two-Step Equations: Example 7TopicSolving Equations DescriptionThis example demonstrates solving the equation 5x - 7 = 18. The solution process involves adding 7 to both sides of the equation, then dividing both sides by 5 to isolate the variable. Through these steps, we find that x = 5. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations: Example 8 | Math Example: Solving Two-Step Equations: Example 8TopicSolving Equations DescriptionThis example demonstrates solving the equation (x/2) - 4 = 8. The solution process involves adding 4 to both sides of the equation, then multiplying both sides by 2 to isolate the variable. Through these steps, we find that x = 24. |
Solving Two-Step Equations |
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Math Example: Solving Two-Step Equations: Example 9 | Math Example: Solving Two-Step Equations: Example 9TopicSolving Equations DescriptionThis example demonstrates solving the equation 3(x + 2) = 12. The solution process involves first dividing both sides of the equation by 3, then subtracting 2 from both sides to isolate the variable. Through these steps, we find that x = 2. |
Solving Two-Step Equations |
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Math Example: Testing Solutions to One-Step Equations--Example 1 | Math Example: Testing Solutions to One-Step Equations--Example 1
This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division. |
Solving One-Step Equations |
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Math Example: Testing Solutions to One-Step Equations--Example 10 | Math Example: Testing Solutions to One-Step Equations--Example 10
This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division. |
Solving One-Step Equations |
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Math Example: Testing Solutions to One-Step Equations--Example 11 | Math Example: Testing Solutions to One-Step Equations--Example 11
This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division. |
Solving One-Step Equations |
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Math Example: Testing Solutions to One-Step Equations--Example 12 | Math Example: Testing Solutions to One-Step Equations--Example 12
This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division. |
Solving One-Step Equations |
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Math Example: Testing Solutions to One-Step Equations--Example 2 | Math Example: Testing Solutions to One-Step Equations--Example 2
This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division. |
Solving One-Step Equations |
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Math Example: Testing Solutions to One-Step Equations--Example 3 | Math Example: Testing Solutions to One-Step Equations--Example 3
This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division. |
Solving One-Step Equations |
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Math Example: Testing Solutions to One-Step Equations--Example 4 | Math Example: Testing Solutions to One-Step Equations--Example 4
This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division. |
Solving One-Step Equations |
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Math Example: Testing Solutions to One-Step Equations--Example 5 | Math Example: Testing Solutions to One-Step Equations--Example 5
This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division. |
Solving One-Step Equations |
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Math Example: Testing Solutions to One-Step Equations--Example 6 | Math Example: Testing Solutions to One-Step Equations--Example 6
This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division. |
Solving One-Step Equations |
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Math Example: Testing Solutions to One-Step Equations--Example 7 | Math Example: Testing Solutions to One-Step Equations--Example 7
This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division. |
Solving One-Step Equations |
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Math Example: Testing Solutions to One-Step Equations--Example 8 | Math Example: Testing Solutions to One-Step Equations--Example 8
This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division. |
Solving One-Step Equations |
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Math Example: Testing Solutions to One-Step Equations--Example 9 | Math Example: Testing Solutions to One-Step Equations--Example 9
This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division. |
Solving One-Step Equations |
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MATH EXAMPLES--Teacher's Guide: Equations of Parallel and Perpendicular Lines | MATH EXAMPLES--Teacher's Guide: Equations of Parallel and Perpendicular Lines
This Teacher's Guide provides an overview of the 32 worked-out examples that show how to find the equation of a line parallel or perpendicular to a given line and through a given point. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Linear Functions and Graphs of Linear Functions |
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MATH EXAMPLES--Teacher's Guide: Finding the Equation of a Line, Given Two Points | MATH EXAMPLES--Teacher's Guide: Finding the Equation of a Line, Given Two Points
This Teacher's Guide provides an overview of the 12 worked-out examples that show how to find the equation of a line, given two points. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Linear Functions and Graphs of Linear Functions |
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MATH EXAMPLES--Teacher's Guide: Rational Expressions | MATH EXAMPLES--Teacher's Guide: Rational Expressions
This Teacher's Guide provides an overview of the 28 worked-out examples that show how to simplify a variety of rational expressions. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Rational Expressions and Rational Functions and Equations |
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MATH EXAMPLES--Teacher's Guide: Solving Equations with Fractions | MATH EXAMPLES--Teacher's Guide: Solving Equations with Fractions
This Teacher's Guide provides an overview of the 13 worked-out examples that solve a variety of one-variable equations with fractions. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Solving Fraction Equations |
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MATH EXAMPLES--Teacher's Guide: Solving Equations with Percents | MATH EXAMPLES--Teacher's Guide: Solving Equations with Percents
What Are Percents?Percents Are a Type of Fraction |
Solving Percent Equations |
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MATH EXAMPLES--Teacher's Guide: Solving One-Variable Equations | MATH EXAMPLES--Teacher's Guide: Solving One-Variable Equations
This Teacher's Guide provides an overview of the 27 worked-out examples that solve a variety of one-variable equations. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Equations and Inequalities |
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MATH EXAMPLES--Teacher's Guide: Solving Quadratic Equations Graphically | MATH EXAMPLES--Teacher's Guide: Solving Quadratic Equations Graphically
This Teacher's Guide provides an overview of the 8 worked-out examples that show how to solve Quadratic Equations graphically. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Quadratic Equations and Functions |
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Math Video Definition 19--Addition and Subtraction Concepts--False Equation | Math Video Definition 19--Addition and Subtraction Concepts--False Equation
TopicAddition and Subtraction DescriptionA False Equation is an equation that displays an incorrect sum or difference. For example, 1 + 1 = 3 and 2 - 1 = 3 are false equations. Identifying false equations sharpens critical thinking and reinforces the importance of accuracy in mathematical reasoning. |
Addition Expressions and Equations |
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Math Video Definition 19--Addition and Subtraction Concepts--False Equation (Spanish Audio) | Math Video Definition 19--Addition and Subtraction Concepts--False Equation (Spanish Audio)
TopicAddition and Subtraction DescriptionDefinition: A False Equation is an equation that displays an incorrect sum or difference. For example, 1 + 1 = 3 and 2 - 1 = 3 are false equations. Identifying false equations sharpens critical thinking and reinforces the importance of accuracy in mathematical reasoning. |
Addition Expressions and Equations |
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Math Video Definition 21--Multiplication and Division Concepts--False Equation | Math Video Definition 21--Multiplication and Division Concepts--False Equation
TopicMultiplication and Division DescriptionA False Equation is an equation that shows an inaccurate product or quotient. For example, 6 x 2 = 10 or 12 ÷ 3 = 5. This concept highlights the importance of verifying calculations for correctness. This term teaches students to identify and avoid common errors in mathematical equations. |
Multiplication Expressions and Equations |
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Math Video Definition 49--Addition and Subtraction Concepts--True Equation | Math Video Definition 49--Addition and Subtraction Concepts--True Equation
TopicAddition and Subtraction DescriptionTrue Equation: An equation that shows an accurate sum or difference. Examples include 5 + 1 = 6 and 4 - 1 = 3. This term reinforces accuracy and verification in arithmetic, ensuring students evaluate equations correctly. |
Addition Expressions and Equations |
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Math Video Definition 49--Addition and Subtraction Concepts--True Equation (Spanish Audio) | Math Video Definition 49--Addition and Subtraction Concepts--True Equation (Spanish Audio)
TopicAddition and Subtraction DescriptionDefinition: True Equation: An equation that shows an accurate sum or difference. Examples include 5 + 1 = 6 and 4 - 1 = 3. This term reinforces accuracy and verification in arithmetic, ensuring students evaluate equations correctly. |
Addition Expressions and Equations |
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Math Video Definition 52--Multiplication and Division Concepts--True Equation | Math Video Definition 52--Multiplication and Division Concepts--True Equation
TopicMultiplication and Division DescriptionA True Equation is an equation that shows an accurate product or quotient. Examples include 5 * 2 = 10 and 8 / 2 = 4. It validates the correctness of mathematical operations. This concept reinforces understanding and application of multiplication and division, focusing on the accuracy of operations. |
Multiplication Expressions and Equations |
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VIDEO: Overview of Variables and Equations | VIDEO: Overview of Variables and Equations
What Is a Variable?A variable is a symbol, usually a letter, that can stand for different things. |
Variable Expressions, Applications of Equations and Inequalities and Variables and Unknowns |
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Paper-and-Pencil Quiz: Equation of a Line Given Two Points (Easy) | Paper-and-Pencil Quiz: Equation of a Line Given Two Points (Easy)
This is part of a collection of math quizzes on the topic of finding the Equation of a Line Given Two Points. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Point-Slope Form and Slope-Intercept Form |
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Paper-and-Pencil Quiz: Equation of a Line Given Two Points (Hard) | Paper-and-Pencil Quiz: Equation of a Line Given Two Points (Hard)
This is part of a collection of math quizzes on the topic of finding the Equation of a Line Given Two Points. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Point-Slope Form and Slope-Intercept Form |
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Paper-and-Pencil Quiz: Equation of a Line Given Two Points (Medium) | Paper-and-Pencil Quiz: Equation of a Line Given Two Points (Medium)
This is part of a collection of math quizzes on the topic of finding the Equation of a Line Given Two Points. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Point-Slope Form and Slope-Intercept Form |
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Paper-and-Pencil Quiz: Equations with Fractions (Easy) | Paper-and-Pencil Quiz: Equations with Fractions (Easy)
This is part of a collection of math quizzes on the topic of Equations with Fractions. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Fraction Equations |
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Paper-and-Pencil Quiz: Equations with Fractions (Hard) | Paper-and-Pencil Quiz: Equations with Fractions (Hard)
This is part of a collection of math quizzes on the topic of Equations with Fractions. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Fraction Equations |
