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Sample Test: Inequalities and Absolute Values

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

Summary: This module provides a sample test on inequalities and absolute values.

Exercise 1

1 < 4 3x 10 1 < 4 3x 10 size 12{1<4 - 3x <= "10"} {}

  • a. Solve for xx size 12{x} {}.
  • b. Draw a number line below, and show where the solution set to this problem is.
  • c. Pick an xx size 12{x} {}-value which, according to your drawing, is inside the solution set. Plug it into the original inequality 1<43x101<43x10 size 12{1<4 - 3x <= "10"} {}. Does the inequality hold true? (Show your work!)
  • d. Pick an xx size 12{x} {}-value which, according to your drawing, is outside the solution set. Plug it into the original inequality 1<43x101<43x10 size 12{1<4 - 3x <= "10"} {}. Does the inequality hold true? (Show your work!)

Exercise 2

Find the xx size 12{x} {} value(s) that make this equation true: 42x+53=1742x+53=17 size 12{4 lline 2x+5 rline - 3="17"} {}

Exercise 3

Find the xx size 12{x} {} value(s) that make this equation true: 5x23=216x5x23=216x size 12{ lline 5x - "23" rline ="21" - 6x} {}

Exercise 4

2x 3 3 + 7 > 9 2x 3 3 + 7 > 9 size 12{ { { lline 2x - 3 rline } over {3} } +7>9} {}

  • a. Solve for xx size 12{x} {}.
  • b. Show graphically where the solution set to this problem is.

Exercise 5

3 x + 4 + 7 7 3 x + 4 + 7 7 size 12{ - 3 lline x+4 rline +7 >= 7} {}

  • a. Solve for xx size 12{x} {}.
  • b. Show graphically where the solution set to this problem is.

Exercise 6

Make up and solve an inequality word problem, having to do with hair.

  • a. Describe the scenario in words.
  • b. Label and clearly describe the variable or variables.
  • c. Write the inequality. (Your answer here should be completely determined by your answers to (a) and (b)—I should know exactly what you’re going to write. If it is not, you probably did not give enough information in your scenario.)

Exercise 7

Graph yx+2yx+2 size 12{y >= - lline x rline +2} {}.

Exercise 8

2y x > 6 2y x > 6 size 12{ lline 2y rline - lline x rline >6} {}

  • a. Rewrite this as an inequality with no absolute values, for the fourth quadrant (lower-right-hand corner of the graph).
  • b. Graph what this looks like, in the fourth quadrant only.

Exercise 9

Graph y=xxy=xx size 12{y=x - lline x rline } {}.

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