2.5 Absolute value inequalities

• 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?

• A

  Write down the solution for what $\mathrm{2x}+3$ has to be. This should look exactly like your answer to number 1, except with a $(\mathrm{2x}+3)$ instead of an $(x)$ .

• B

  Now, solve that inequality for $x$ .

• 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?

$4\mid \mathrm{3x}-6\mid +7>\text{19}$

• A

  Solve for $\mid \mathrm{3x}-6\mid$ . (That is, leave the $\mid \mathrm{3x}-6\mid$ part alone, but get rid of all the stuff around it.)

• B

  Write down the inequality for what $(\mathrm{3x}-6)$ has to be.

• C

  Now, solve that inequality for $x$ .

• 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?

• A

  Solve for $x$ . (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?

$6\mid {\mathrm{2x}}^2-\text{17}x-\text{85}\mid +5\ge 3$

• A

  Solve for $x$ .

• 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?