Solve the Linear Equation: -8(2x + 4) = 6(x - 4) + 3

Q: Why do I distribute first instead of trying to isolate x immediately?

You must distribute first because the variable x is trapped inside parentheses. You can't isolate what you can't access! Distribution removes the parentheses so you can see all the x-terms clearly.

Q: How do I keep track of positive and negative signs when distributing?

Write out each multiplication step: -8 × 2x = -16x and -8 × 4 = -32. When the outside number is negative, it changes the sign of every term inside the parentheses.

Q: What's the difference between moving terms and distributing?

Distribution removes parentheses by multiplying. Moving terms comes after - you add or subtract the same amount from both sides to collect like terms.

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

Substitute $ x = -\frac{1}{2} $ back into the original equation. Calculate both sides carefully - they should both equal the same number when your answer is correct.

Linear Equations with Distribution and Combination

Solve for x:

$-8(2x+4)=6(x-4)+3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:05 Open parentheses properly, multiply by each factor

00:26 Collect like terms

00:33 Arrange the equation so that X is isolated on one side

00:51 Collect like terms

01:00 Isolate X

01:10 Factor 22 into 11 and 2

01:16 Simplify as much as possible

01:20 This is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for x:

$-8(2x+4)=6(x-4)+3$

Step-by-step solution

To open parentheses we will use the formula:

$a\left(x+b\right)=ax+ab$

$(-8\times2x)+(-8\times4)=(6\times x)+(6\times-4)+3$

We multiply accordingly:

$-16x-32=6x-24+3$

Calculate the elements on the right section:

$-16x-32=6x-21$

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

$-32+21=6x+16x$

Calculate the elements accordingly

$-11=22x$

We divide the two sections by 22

$-\frac{11}{22}=\frac{22x}{22}$

$-\frac{1}{2}=x$

Final Answer

$-\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Distribution: Apply distributive property to both sides before combining terms
Technique: Move all x-terms left, constants right: -16x - 6x = -21 + 32
Check: Substitute $x = -\frac{1}{2}$ into original equation: both sides equal $-24$ ✓

Common Mistakes

Avoid these frequent errors

Incorrectly distributing negative signs
Don't forget to distribute the negative sign: -8(2x + 4) becomes -16x - 32, not -16x + 32! Missing the negative creates wrong coefficients. Always multiply each term inside parentheses by the outside coefficient, keeping track of positive and negative signs.

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 distribute first instead of trying to isolate x immediately?

You must distribute first because the variable x is trapped inside parentheses. You can't isolate what you can't access! Distribution removes the parentheses so you can see all the x-terms clearly.

How do I keep track of positive and negative signs when distributing?

Write out each multiplication step: -8 × 2x = -16x and -8 × 4 = -32. When the outside number is negative, it changes the sign of every term inside the parentheses.

What's the difference between moving terms and distributing?

Distribution removes parentheses by multiplying. Moving terms comes after - you add or subtract the same amount from both sides to collect like terms.

Why did my answer come out as a fraction?

Fractions are completely normal answers! When you divide -11 by 22, you get $-\frac{11}{22} = -\frac{1}{2}$ . Always simplify fractions to lowest terms.

How can I check if my fraction answer is correct?

Substitute $x = -\frac{1}{2}$ back into the original equation. Calculate both sides carefully - they should both equal the same number when your answer is correct.

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