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Collection by: Kenny M. Felder. E-mail the author

# Absolute Value Inequalities

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides sample problems which develop concepts related to absolute value inequalities.

## Exercise 1

x 7 x 7 size 12{ lline x rline <= 7} {}

• a. Solve.
• b. Graph your solution on a number line
• c. Choose a point that is in your solution set, and test it in the original inequality. Does it work?
• d. Choose a point that is not in your solution set, and test it in the original inequality. Does it work?

## Exercise 2

2x + 3 7 2x + 3 7 size 12{ lline 2x+3 rline <= 7} {}

• a. Write down the solution for what 2x+32x+3 size 12{2x+3} {} has to be. This should look exactly like your answer to number 1, except with a (2x+3)(2x+3) size 12{ $$2x+3$$ } {} instead of an (x)(x) size 12{ $$x$$ } {}.
• b. Now, solve that inequality for xx size 12{x} {}.
• c. Graph your solution on a number line
• d. Choose a point that is in your solution set, and test it in the original inequality. Does it work?
• e. Choose a point that is not in your solution set, and test it in the original inequality. Does it work?

## Exercise 3

4 3x 6 + 7 > 19 4 3x 6 + 7 > 19 size 12{4 lline 3x - 6 rline +7>"19"} {}

• a. Solve for 3x63x6 size 12{ lline 3x - 6 rline } {}. (That is, leave the 3x63x6 size 12{ lline 3x - 6 rline } {} part alone, but get rid of all the stuff around it.)
• b. Write down the inequality for what (3x6)(3x6) size 12{ $$3x - 6$$ } {} has to be.
• c. Now, solve that inequality for xx size 12{x} {}.
• d. Graph your solution on a number line
• e. Choose a point that is in your solution set, and test it in the original inequality. Does it work?
• f. Choose a point that is not in your solution set, and test it in the original inequality. Does it work?

## Exercise 4

3x 4 2 + 6 < 3 3x 4 2 + 6 < 3 size 12{ { { lline 3x - 4 rline } over {2} } +6<3} {}

• a. Solve for xx size 12{x} {}. (You know the drill by now!)
• b. Graph your solution on a number line
• c. Choose a point that is in your solution set, and test it in the original inequality. Does it work?
• d. Choose a point that is not in your solution set, and test it in the original inequality. Does it work?

## Exercise 5

6 2x 2 17 x 85 + 5 3 6 2x 2 17 x 85 + 5 3 size 12{6 lline 2x rSup { size 8{2} } - "17"x - "85" rline +5 >= 3} {}

• a. Solve for xx size 12{x} {}.
• b. Graph your solution on a number line
• c. Choose a point that is in your solution set, and test it in the original inequality. Does it work?
• d. Choose a point that is not in your solution set, and test it in the original inequality. Does it work?

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