Solve the Absolute Value Equation: |-2x| = 16

Q: Why do I need to solve two separate equations?

Because absolute value represents distance from zero, which is always positive! The expression inside can be either positive or negative, but both give the same absolute value. So $ |-2x| = 16 $ means -2x could equal 16 OR -16.

Q: How do I know which equation to set up?

For any equation $ |A| = B $, always write: A = B and A = -B. In our case, A is -2x and B is 16, so we get -2x = 16 and -2x = -16.

Q: Can the absolute value ever equal a negative number?

Never! Absolute values are always zero or positive. If you see something like $ |x| = -5 $, there's no solution because distances can't be negative.

Q: How do I check if both answers are correct?

Substitute each answer back into the original equation. For x = -8: $ |-2(-8)| = |16| = 16 $ ✓. For x = 8: $ |-2(8)| = |-16| = 16 $ ✓. Both work!

Absolute Value Equations with Negative Coefficients

$\left|-2x\right|=16$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\left|-2x\right|=16$

Step-by-step solution

To solve the equation $\left|-2x\right|=16$ , we consider the definition of absolute value:

1. The expression inside the absolute value can be either positive or negative, but its absolute value is always positive.

2. Therefore, we set up two equations to solve:

$-2x = 16$ and $-2x = -16$

3. Solving the first equation:

$-2x = 16$

4. Divide both sides by -2:

$x = -8$

5. Solving the second equation:

$-2x = -16$

6. Divide both sides by -2:

$x = 8$

7. Therefore, the solution is:

$x=-8$ , $x=8$

Final Answer

$x=-8$ , $x=8$

Key Points to Remember

Essential concepts to master this topic

Definition: Absolute value equals the distance from zero, always positive
Technique: Set up two equations: -2x = 16 and -2x = -16
Check: Substitute both solutions: |-2(-8)| = 16 and |-2(8)| = 16 ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative case when solving absolute value equations
Don't just solve -2x = 16 to get x = -8! This gives you only half the solution and misses x = 8. Always remember that |A| = B means A = B OR A = -B, so you need both equations.

Practice Quiz

Test your knowledge with interactive questions

$\left|-x\right|=10$

FAQ

Everything you need to know about this question

Why do I need to solve two separate equations?

Because absolute value represents distance from zero, which is always positive! The expression inside can be either positive or negative, but both give the same absolute value. So $|-2x| = 16$ means -2x could equal 16 OR -16.

How do I know which equation to set up?

For any equation $|A| = B$ , always write: A = B and A = -B. In our case, A is -2x and B is 16, so we get -2x = 16 and -2x = -16.

What if I get the same answer from both equations?

That's possible! Sometimes absolute value equations have only one solution. For example, $|x| = 0$ only gives x = 0. Always solve both cases to be sure.

Can the absolute value ever equal a negative number?

Never! Absolute values are always zero or positive. If you see something like $|x| = -5$ , there's no solution because distances can't be negative.

How do I check if both answers are correct?

Substitute each answer back into the original equation. For x = -8: $|-2(-8)| = |16| = 16$ ✓. For x = 8: $|-2(8)| = |-16| = 16$ ✓. Both work!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Absolute Value and Inequality questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime