Solve Linear Equation: (x-4)×3 = 2(x+6) Step-by-Step

Q: Why do I need to use the distributive property first?

The distributive property removes parentheses so you can see all terms clearly. Without it, you can't combine like terms or solve the equation properly!

Q: What if I get confused about which terms to move?

Remember: move all x terms to one side and all number terms to the other side. This separates variables from constants, making it easier to solve.

Q: How do I know if I distributed correctly?

Check that you multiplied the outside number by every term inside the parentheses. For $ 3(x-4) $, you should get $ 3x - 12 $, not just $ 3x $.

Q: Why do I add 12 to both sides at the end?

You're isolating the variable x. Since you have $ x - 12 = 12 $, adding 12 to both sides cancels out the -12 on the left, leaving just x.

Linear Equations with Distributive Property

Solve for x:

$(x-4)\cdot3=2(x+6)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Open brackets properly, multiply by each factor

00:19 Arrange the equation so that only the unknown X is on one side

00:36 Collect like terms

00:40 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:

$(x-4)\cdot3=2(x+6)$

Step-by-step solution

To solve the equation $(x-4)\cdot3=2(x+6)$ , we'll follow a systematic approach:

Step 1: Apply the distributive property to both sides of the equation.

On the left side: $3(x-4) = 3x - 12$
On the right side: $2(x+6) = 2x + 12$

Step 2: Rewrite the equation with the expanded terms:
$3x - 12 = 2x + 12$

Step 3: Move all terms involving $x$ to one side and constant terms to the other.

Subtract $2x$ from both sides to move $x$ terms to the left:
$3x - 2x = 12 + 12$ which simplifies to $x - 12 = 12$ .
Add 12 to both sides to isolate $x$ :
$x = 24$ .

Therefore, the solution to the equation is $x = 24$ .

Final Answer

$24$

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Multiply terms inside parentheses by outside coefficient
Technique: $3(x-4) = 3x - 12$ and $2(x+6) = 2x + 12$
Check: Substitute $x = 24$ : $3(20) = 60$ and $2(30) = 60$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute to all terms inside parentheses
Don't just multiply 3 × x and forget the -4 = wrong equation! This leaves out part of the expression and gives incorrect results. Always multiply the outside number by every single term inside the parentheses.

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 use the distributive property first?

The distributive property removes parentheses so you can see all terms clearly. Without it, you can't combine like terms or solve the equation properly!

What if I get confused about which terms to move?

Remember: move all x terms to one side and all number terms to the other side. This separates variables from constants, making it easier to solve.

How do I know if I distributed correctly?

Check that you multiplied the outside number by every term inside the parentheses. For $3(x-4)$ , you should get $3x - 12$ , not just $3x$ .

Can I solve this equation a different way?

Yes! You could divide both sides by their common factors first, but the distributive property method is usually clearer and less prone to errors.

What if my final answer seems too big?

Don't worry about the size of your answer! Large numbers like 24 can be correct. Always verify by substituting back into the original equation.

Why do I add 12 to both sides at the end?

You're isolating the variable x. Since you have $x - 12 = 12$ , adding 12 to both sides cancels out the -12 on the left, leaving just x.

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