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Solving One-Variable Inequalities: Techniques and Examples

In this lesson, you will learn how to solve one-variable inequalities using additive and multiplicative inverses. We will explore properties of inequalities, such as the Addition and Multiplication Properties of Inequality, and apply them to solve examples like -4(x - 5) > 2x + 10. Additionally, you'll discover the importance of switching the direction of the inequality sign when multiplying or dividing by a negative number. By the end of this lesson, you'll be equipped with the skills to solve various one-variable inequalities confidently.

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Solving One-Variable Inequalities: Techniques and Examples

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  1. How do you solve one-variable inequalities? For example, how do you know what values of x make the following inequality true? -4(x – 5) > 2x + 10

  2. In this lesson you will learn how to solve inequalities by using additive and multiplicative inverses.

  3. Addition Property of Inequality 2 + + 2 4 < 5 6 < 7 (-2) + + (-2) 4 < 5 2 < 3

  4. Multiplication Property of Inequality 2 xx 2 4 < 5 8 < 10 (-2) xx (-2) 4 < 5 -8 <-10 -8 > -10

  5. Forgetting that the multiplication property of inequality may mean that you need to switch the direction of the inequality sign. x- 1 1 -4x > 16 4 4 x- x < -4

  6. x # 3x > 2x + 7 -2x -2x Check: x = 9 x > 7 9 > 7 3(9) > 2(9) + 7

  7. x # -4(x – 5) < 2x + 8 Check: -4x + 20 < 2x + 8 x- -20 -20 x = 5 -4x < 2x - 12 5 > 2 1 1 -2x -2x 6 6 -4(5 – 5) < 2(5) + 10 -6x < -12 x- x > 2

  8. In this lesson you have learned how to solve inequalities by using additive and multiplicative inverses.

  9. 4x – 15 > -3(8 – 4x)

  10. Please add extension activity • Describe one extension activity here…

  11. Describe another extension activity here…

  12. 5x + 23 < 3 – 4x + 2 4x – 7x + 2 > 4 + 5x

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