2.3 Absolute value equations

$\mid 4\mid =$

$\mid -5\mid =$

$\mid 0\mid =$

OK, now, I’m thinking of a number. All I will tell you is that the absolute value of my number is 7.

• A

  Rewrite my question as a math equation instead of a word problem.

• B

  What can my number be?

I’m thinking of a different number. This time, the absolute value of my number is 0.

• A

  Rewrite my question as a math equation instead of a word problem.

• B

  What can my number be?

I’m thinking of a different number. This time, the absolute value of my number is –4.

• A

  Rewrite my question as a math equation instead of a word problem.

• B

  What can my number be?

I’m thinking of a different number. This time, the absolute value of my number is less than 7.

• A

  Rewrite my question as a math inequality instead of a word problem.

• B

  Does 8 work?

• C

  Does 6 work?

• D

  Does $-8$ work?

• E

  Does $-6$ work?

• F

  Write an inequality that describes all possible values for my number.

I’m thinking of a different number. This time, the absolute value of my number is greater than 4.

• A

  Rewrite my question as a math inequality instead of a word problem.

• B

  Write an inequality that describes all possible values for my number. (Try a few numbers, as we did in #7.)

I’m thinking of a different number. This time, the absolute value of my number is greater than $-4$ .

• A

  Rewrite my question as a math inequality instead of a word problem.

• B

  Write an inequality that describes all possible values for my number.

$\mid x+3\mid =7$

• A

  First, forget that it says“ $x+3$ ”and just think of it as“a number.”The absolute value of this number is 7. So what can this number be?

• B

  Now, remember that“this number”is $x+3$ . So write an equation that says that $x+3$ can be <your answer(s) in part (a)>.

• C

  Solve the equation(s) to find what $x$ can be.

• D

  Plug your answer(s) back into the original equation $\mid x+3\mid =7$ and see if they work.

$4\mid \mathrm{3x}-2\mid +5=\text{17}$

• A

  This time, because the absolute value is not alone, we’re going to start with some algebra. Leave $\mid \mathrm{3x}-2\mid$ alone, but get rid of everything around it, so you end up with $\mid \mathrm{3x}-2\mid$ alone on the left side, and some other number on the right.

• B

  Now, remember that“some number”is $\mathrm{3x}-2$ . So write an equation that says that $\mathrm{3x}-2$ can be <your answer(s) in part a> .

• C

  Solve the equation(s) to find what $x$ can be.

• D

  Plug your answer(s) back into the original equation $4\mid \mathrm{3x}-2\mid +5=\text{17}$ and see if they work.

$\mid \mathrm{3x}-3\mid +5=4$

• A

  Solve, by analogy to the way you solved the last two problems.

• B

  Plug your answer(s) back into the original equation $\mid \mathrm{3x}-3\mid +5=4$ and see if they work.

$\mid x-2\mid =\mathrm{2x}-\text{10}$ .

• A

  Solve, by analogy to the way you solved the last two problems.

• B

  Plug your answer(s) back into the original equation $\mid x-2\mid =\mathrm{2x}-\text{10}$ and see if they work.