Solve for X in the Linear Equation: 3x + 6 = 12

Q: Why do I subtract 6 first instead of dividing by 3?

You must follow the reverse order of operations! Since addition happens after multiplication in $ 3x + 6 $, you undo addition first by subtracting 6, then undo multiplication by dividing by 3.

Q: What if I accidentally divide first?

You'll get $ x + 2 = 4 $, which still works but creates unnecessary fractions in harder problems. It's better to always handle addition and subtraction before multiplication and division.

Q: How do I remember which operation to do first?

Think PEMDAS backwards! To solve equations, undo operations in reverse order: first addition/subtraction, then multiplication/division, just like peeling layers off an onion.

Q: What does 'isolate the variable' actually mean?

It means getting the variable by itself on one side of the equation. You want $ x = \text{number} $, not $ 3x + 6 = 12 $.

Q: Can I check my answer a different way?

Yes! You can also work backwards: if $ x = 2 $, then $ 3 \times 2 = 6 $, and $ 6 + 6 = 12 $. Both methods should give you the same result!

Linear Equations with Two-Step Isolation

Solve for X:

$3x + 6 = 12$

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Understand the problem

Solve for X:

$3x + 6 = 12$

Step-by-step solution

Step-by-step solution:

1. Start with the equation: $3x + 6 = 12$

2. Subtract 6 from both sides: $3x + 6 - 6 = 12 - 6$ , which simplifies to $3x = 6$

3. Divide both sides by 3 to solve for x: $x = \frac{6}{3}$

4. Simplify the division: $x = 2$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Undo operations in reverse order using inverse operations
Technique: First subtract 6, then divide by 3: $3x = 6$ becomes $x = 2$
Check: Substitute back: $3(2) + 6 = 6 + 6 = 12$ ✓

Common Mistakes

Avoid these frequent errors

Dividing before subtracting the constant term
Don't divide 3x + 6 = 12 by 3 first to get x + 2 = 4! This creates harder fractions and confuses the process. Always subtract or add constant terms first, then multiply or divide to isolate the variable.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why do I subtract 6 first instead of dividing by 3?

You must follow the reverse order of operations! Since addition happens after multiplication in $3x + 6$ , you undo addition first by subtracting 6, then undo multiplication by dividing by 3.

What if I accidentally divide first?

You'll get $x + 2 = 4$ , which still works but creates unnecessary fractions in harder problems. It's better to always handle addition and subtraction before multiplication and division.

How do I remember which operation to do first?

Think PEMDAS backwards! To solve equations, undo operations in reverse order: first addition/subtraction, then multiplication/division, just like peeling layers off an onion.

What does 'isolate the variable' actually mean?

It means getting the variable by itself on one side of the equation. You want $x = \text{number}$ , not $3x + 6 = 12$ .

Can I check my answer a different way?

Yes! You can also work backwards: if $x = 2$ , then $3 \times 2 = 6$ , and $6 + 6 = 12$ . Both methods should give you the same result!

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