Solve for X in the Equation 8(-2-x)=16: Step-by-Step Guide

Q: Why do we divide both sides by 8 first?

Dividing by 8 first simplifies the equation by eliminating the coefficient outside the parentheses. This makes it easier to work with the expression inside: $ -2-x = 2 $

Q: What does 'move -2 to the right side' actually mean?

It means add 2 to both sides of the equation! When we have $ -2-x = 2 $, adding 2 to both sides gives us $ -x = 4 $.

Q: Why is my final answer negative?

The answer x = -4 is correct! Negative solutions are common in algebra. Always trust your work if you followed the steps correctly and your check proves it's right.

Q: Can I distribute the 8 first instead of dividing?

Yes, you can! Distributing gives: $ 8(-2) + 8(-x) = 16 $, which becomes $ -16 - 8x = 16 $. Both methods work - choose what feels easier!

Q: How do I remember to divide by -1 at the end?

Remember: you want positive x, not negative x! If you see -x = [number], always divide both sides by -1 to flip the signs and get your final answer.

Linear Equations with Distributive Property

Solve for x:

$8(-2-x)=16$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's find the value of X.

00:10 First, divide by 8. This removes the coefficient from the parentheses.

00:21 Next, simplify as much as you can.

00:26 Rearrange the equation. Make sure X is only on one side.

00:33 Now, combine all similar terms.

00:36 Change negatives to positives if needed.

00:44 Remember, a negative divided by a negative becomes positive, and the opposite is true.

00:50 Great job! Here's your solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for x:

$8(-2-x)=16$

Step-by-step solution

First, we divide both sections by 8:

$\frac{8(-2-x)}{8}=\frac{16}{8}$

Keep in mind that the 8 in the fraction of the left section is reduced, so the equation we get is:

$-2-x=2$

We move the minus 2 to the right section and maintain the plus and minus signs accordingly:

$-x=2+2$

$-x=4$

We divide both sides by minus 1 and maintain the plus and minus signs accordingly when we divide:

$\frac{-x}{-1}=\frac{4}{-1}$

$x=-4$

Final Answer

-4

Key Points to Remember

Essential concepts to master this topic

Division Rule: Divide both sides by the same coefficient first
Technique: Isolate variable by moving constants: -x = 4 becomes x = -4
Check: Substitute x = -4: 8(-2-(-4)) = 8(2) = 16 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to change signs when dividing by negative one
Don't leave -x = 4 as your final answer = wrong solution! When you have -x, you must divide both sides by -1 to get positive x. Always remember: dividing by -1 changes the sign of both sides.

Practice Quiz

Test your knowledge with interactive questions

$$ x+x=8 $$

FAQ

Everything you need to know about this question

Why do we divide both sides by 8 first?

Dividing by 8 first simplifies the equation by eliminating the coefficient outside the parentheses. This makes it easier to work with the expression inside: $-2-x = 2$

What does 'move -2 to the right side' actually mean?

It means add 2 to both sides of the equation! When we have $-2-x = 2$ , adding 2 to both sides gives us $-x = 4$ .

Why is my final answer negative?

The answer x = -4 is correct! Negative solutions are common in algebra. Always trust your work if you followed the steps correctly and your check proves it's right.

Can I distribute the 8 first instead of dividing?

Yes, you can! Distributing gives: $8(-2) + 8(-x) = 16$ , which becomes $-16 - 8x = 16$ . Both methods work - choose what feels easier!

How do I remember to divide by -1 at the end?

Remember: you want positive x, not negative x! If you see -x = [number], always divide both sides by -1 to flip the signs and get your final answer.

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