Solve the Linear Equation: 6(5+2x)=3x-6 Step by Step

Q: What does it mean to 'distribute' in algebra?

Distribution means multiplying the number outside parentheses by every term inside. So $ 6(5+2x) $ becomes $ 6 \times 5 + 6 \times 2x = 30 + 12x $.

Q: Why do I subtract 3x from both sides instead of adding?

We want to get all x terms on one side. Since we have +12x on the left and +3x on the right, subtracting 3x from both sides gives us $ 12x - 3x = 9x $ on the left and eliminates x from the right.

Q: What if I get a negative answer like -4?

Negative answers are completely normal! Always double-check by substituting back into the original equation. If both sides equal the same number, your negative answer is correct.

Linear Equations with Distribution and Combining Terms

Solve for X:

$6\cdot(5+2x)=3x-6$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 We want to isolate the unknown X

00:08 Open parentheses properly, multiply by each factor

00:17 Solve each multiplication separately

00:39 Isolate the unknown X

00:58 Reduce what we can

01:03 Combine terms

01:15 Isolate the unknown X

01:28 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$6\cdot(5+2x)=3x-6$

Step-by-step solution

To solve the equation $6\cdot(5+2x)=3x-6$ , we will proceed as follows:

Step 1: Distribute the 6 within the parentheses on the left side:
$6\cdot(5+2x) = 30 + 12x$ .
Step 2: Substitute the distributed expression into the equation:
$30 + 12x = 3x - 6$ .
Step 3: Isolate the variable terms on one side:
Subtract $3x$ from both sides: $30 + 12x - 3x = -6$ , which simplifies to $30 + 9x = -6$ .
Step 4: Isolate the term containing $x$ :
Subtract 30 from both sides: $9x = -6 - 30$ , which simplifies to $9x = -36$ .
Step 5: Solve for $x$ by dividing both sides by 9:
$x = \frac{-36}{9} = -4$ .

Therefore, the solution to the equation is $x = -4$ , which corresponds to choice 1.

Final Answer

$-4$

Key Points to Remember

Essential concepts to master this topic

Distribution: Multiply 6 through parentheses: 6(5+2x) = 30 + 12x
Technique: Collect like terms: 12x - 3x = 9x on left side
Check: Substitute x = -4: 6(5 + 2(-4)) = 6(-3) = -18 = 3(-4) - 6 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute to all terms inside parentheses
Don't multiply 6 × 5 but forget 6 × 2x = wrong equation setup! This gives 30 + 2x = 3x - 6 instead of 30 + 12x = 3x - 6, leading to x = 36 instead of x = -4. Always distribute the outside number to every term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

$$ 11=a-16 $$

$a=\text{?}$

FAQ

Everything you need to know about this question

What does it mean to 'distribute' in algebra?

Distribution means multiplying the number outside parentheses by every term inside. So $6(5+2x)$ becomes $6 \times 5 + 6 \times 2x = 30 + 12x$ .

Why do I subtract 3x from both sides instead of adding?

We want to get all x terms on one side. Since we have +12x on the left and +3x on the right, subtracting 3x from both sides gives us $12x - 3x = 9x$ on the left and eliminates x from the right.

How do I know which side to move the x terms to?

It doesn't matter! You can move them to either side. Most students find it easier to move terms so the coefficient of x is positive, but both ways give the same answer.

What if I get a negative answer like -4?

Negative answers are completely normal! Always double-check by substituting back into the original equation. If both sides equal the same number, your negative answer is correct.

Can I solve this equation a different way?

Yes! You could subtract 30 from both sides first, or add 6 to both sides first. Multiple approaches work as long as you perform the same operation to both sides each step.

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