2.9 Sample test: inequalities and absolute values

• A

  Solve for $x$ .

• B

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

• C

  Pick an $x$ -value which, according to your drawing, is inside the solution set. Plug it into the original inequality . Does the inequality hold true? (Show your work!)

• D

  Pick an $x$ -value which, according to your drawing, is outside the solution set. Plug it into the original inequality . Does the inequality hold true? (Show your work!)

Find the $x$ value(s) that make this equation true: $4\mid \mathrm{2x}+5\mid -3=\text{17}$

Find the $x$ value(s) that make this equation true: $\mid \mathrm{5x}-\text{23}\mid =\text{21}-\mathrm{6x}$

$\frac{\mid \mathrm{2x}-3\mid }{3}+7>9$

• A

  Solve for $x$ .

• B

  Show graphically where the solution set to this problem is.

$-3\mid x+4\mid +7\ge 7$

• A

  Solve for $x$ .

• B

  Show graphically where the solution set to this problem is.

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.)

Graph $y\ge -\mid x\mid +2$ .

$\mid \mathrm{2y}\mid -\mid x\mid >6$

• 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.

Graph $y=x-\mid x\mid$ .