How do you solve one-variable inequalities?
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Transcript of How do you solve one-variable inequalities?
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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
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In this lesson you will learn how to solve inequalities by
using additive and multiplicative inverses.
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Let’s Review
Addition Property of Inequality
4 < 5 2 + + 26 < 7
4 < 5 (-2) + + (-2)
2 < 3
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Let’s Review
Multiplication Property of Inequality4 < 52 x x 28 < 10
4 < 5(-2) x x (-2)
-8 <-10-8 > -10
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A Common Mistake
Forgetting that the multiplication property of inequality may mean that you need to switch the direction of the
inequality sign.
-4x > 16 x - 1
4 14
x -
x < -4
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Core Lesson x #3x > 2x + 7-2x -2x
x > 7
Check:x = 9
3(9) > 2(9) + 7
9 > 7
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Core Lesson -4(x – 5) < 2x + 8 -4x + 20 < 2x + 8
x #
-20 -20
-4x < 2x - 12-2x -2x
-6x < -12
x > 2
Check:
-4(5 – 5) < 2(5) + 10
x = 5
5 > 2
x - 16
16
x -
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In this lesson you have learned how to solve inequalities by
using additive and multiplicative inverses.
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Guided Practice
4x – 15 > -3(8 – 4x)
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Extension Activities
Describe one extension activity here…
Please add extension activity
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Extension Activities
Describe another extension activity here…
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Quick Quiz
5x + 23 < 3 – 4x + 2
4x – 7x + 2 > 4 + 5x