Solve for X in 8(x-2) = -4(x+3): Linear Equation with Brackets

Q: How do I remember which direction to move terms?

Use the rule: variables go left, numbers go right. When moving terms, always change their signs. Think of it as 'undoing' the operation.

Q: How can I check if my fraction answer is correct?

Substitute your fraction back into the original equation. Both sides should give you the same value. For example: $ 8(\frac{1}{3}-2) = -4(\frac{1}{3}+3) $ both equal $ -\frac{32}{3} $.

Linear Equations with Distributive Property

Solve for x:

$8(x-2)=-4(x+3)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's find X, together.

00:13 First, open the parentheses carefully. Multiply each term inside, with each factor outside.

00:31 Then, rearrange the equation, so all terms with X are on one side.

00:48 Next, combine any like terms, to simplify the equation.

00:53 Now, isolate X by moving other numbers to the opposite side.

01:03 Let's factor twelve into four, and three.

01:08 Simplify the equation, as much as you can.

01:12 Great work! And that's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for x:

$8(x-2)=-4(x+3)$

Step-by-step solution

To open parentheses we will use the formula:

$a(x+b)=ax+ab$

$(8\times x)+(8\times-2)=(-4\times x)+(-4\times3)$

We multiply accordingly

$8x-16=-4x-12$

In the left section we enter the elements with the X and in the right section those without the X, remember to change the plus and minus signs as appropriate when transferring:

$8x+4x=-12+16$

We solve accordingly

$12x=4$

We divide both sections by 12

$\frac{12x}{12}=\frac{4}{12}$

We reduce and obtain $x=\frac{4}{12}=\frac{1}{3}$

Final Answer

$\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Distribution: Multiply each term inside brackets by coefficient outside
Technique: Move variables left and constants right: 8x + 4x = 4
Check: Substitute $\frac{1}{3}$ into original equation: both sides equal $-\frac{32}{3}$ ✓

Common Mistakes

Avoid these frequent errors

Not changing signs when moving terms across equals sign
Don't just copy 8x - 16 = -4x - 12 to get 8x - 4x = -12 - 16 = wrong answer! When moving terms across the equals sign, you must change their signs. Always flip the sign: +4x becomes -4x, and -16 becomes +16.

Practice Quiz

Test your knowledge with interactive questions

Solve for x:

$$ 2(4-x)=8 $$

FAQ

Everything you need to know about this question

Why do I need to distribute first before solving?

Distribution eliminates the brackets so you can see all terms clearly. Without distributing 8(x-2) properly, you can't collect like terms or move variables to one side.

How do I remember which direction to move terms?

Use the rule: variables go left, numbers go right. When moving terms, always change their signs. Think of it as 'undoing' the operation.

What if I get a fraction as my answer?

That's completely normal! Many linear equations have fractional solutions. Just make sure to reduce the fraction to lowest terms like $\frac{4}{12} = \frac{1}{3}$ .

How can I check if my fraction answer is correct?

Substitute your fraction back into the original equation. Both sides should give you the same value. For example: $8(\frac{1}{3}-2) = -4(\frac{1}{3}+3)$ both equal $-\frac{32}{3}$ .

Why did we collect variables on the left side?

It's just convention - you can collect them on either side! The key is to pick one side and stick with it. Most people choose left side because we read from left to right.

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