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

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

  • A

    Solve for x size 12{x} {} .
  • B

    Draw a number line below, and show where the solution set to this problem is.
  • C

    Pick an x size 12{x} {} -value which, according to your drawing, is inside the solution set. Plug it into the original inequality 1 < 4 3x 10 size 12{1<4 - 3x<= "10"} {} . Does the inequality hold true? (Show your work!)
  • D

    Pick an x size 12{x} {} -value which, according to your drawing, is outside the solution set. Plug it into the original inequality 1 < 4 3x 10 size 12{1<4 - 3x<= "10"} {} . Does the inequality hold true? (Show your work!)
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Find the x size 12{x} {} value(s) that make this equation true: 4 2x + 5 3 = 17 size 12{4 lline 2x+5 rline - 3="17"} {}

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

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

  • A

    Solve for x size 12{x} {} .
  • B

    Show graphically where the solution set to this problem is.
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3 x + 4 + 7 7 size 12{ - 3 lline x+4 rline +7>= 7} {}

  • A

    Solve for x size 12{x} {} .
  • B

    Show graphically where the solution set to this problem is.
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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.)
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Graph y x + 2 size 12{y>= - lline x rline +2} {} .

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

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Source:  OpenStax, Advanced algebra ii: activities and homework. OpenStax CNX. Sep 15, 2009 Download for free at http://cnx.org/content/col10686/1.5
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