Solve the Fraction Equation: Find X in 1/6(x-4) = 1/4(1/3x+3)

Q: Why multiply by 12 instead of just clearing one fraction at a time?

Using the LCD (12) clears all fractions in one step! If you clear fractions one at a time, you create new fractions that make the problem more complicated.

Q: How do I handle the fraction inside parentheses like 1/3x?

When you multiply by the LCD, distribute it to every term. So $ 12 \times \frac{1}{4}(\frac{1}{3}x + 3) $ becomes $ 3(\frac{1}{3}x + 3) $, then distribute again!

Q: What if I get confused with all the fractions?

Break it down step by step: identify all denominators (6, 4, 3), find their LCD (12), then multiply everything by 12. Take your time with each step!

Q: How do I verify my answer with all these fractions?

Substitute x = 17 into the original equation. Calculate each side separately: left side gives $ \frac{13}{6} $, right side also gives $ \frac{13}{6} $. Equal values confirm your answer!

Linear Equations with Nested Fractions

Solve for X:

$\frac{1}{6}(x-4)=\frac{1}{4}(\frac{1}{3}x+3)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Multiply by the common denominator, and multiply accordingly

00:17 Open parentheses properly, multiply by each factor

00:39 Simplify what we can

00:42 Arrange the equation so that one side has only the unknown X

00:54 Collect like terms

01:00 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:

$\frac{1}{6}(x-4)=\frac{1}{4}(\frac{1}{3}x+3)$

Step-by-step solution

To solve the equation $\frac{1}{6}(x-4) = \frac{1}{4}(\frac{1}{3}x+3)$ , follow these steps:

Step 1: Clear fractions by finding a common multiple.
The least common multiple of 6 and 4 is 12. Multiply both sides by 12 to eliminate the fractions.
$12 \times \left( \frac{1}{6} \right)(x-4) = 12 \times \left( \frac{1}{4} \right)\left( \frac{1}{3}x + 3 \right)$ .
Step 2: Simplify both sides.
On the left side: $2(x-4) = 2x - 8$ .
On the right side: $3\left( \frac{1}{3}x + 3 \right) = x + 9$ .
Step 3: Set the simplified expressions equal.
$2x - 8 = x + 9$ .
Step 4: Solve the linear equation for $x$ .
Subtract $x$ from both sides: $2x - x = 9 + 8$ .
This simplifies to $x = 17$ .

Therefore, the solution to the equation is $x = 17$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Find LCD to eliminate all fractions simultaneously
Technique: Multiply by 12: $12 \times \frac{1}{6} = 2$ and $12 \times \frac{1}{4} = 3$
Check: Substitute x = 17: $\frac{1}{6}(13) = \frac{1}{4}(\frac{17}{3} + 3)$ gives equal values ✓

Common Mistakes

Avoid these frequent errors

Not multiplying all terms by the LCD
Don't multiply only the fraction coefficients by 12 and forget the terms inside parentheses = wrong equation! This creates unequal expressions that don't represent the original problem. Always distribute the LCD to every single term on both sides.

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 multiply by 12 instead of just clearing one fraction at a time?

Using the LCD (12) clears all fractions in one step! If you clear fractions one at a time, you create new fractions that make the problem more complicated.

How do I handle the fraction inside parentheses like 1/3x?

When you multiply by the LCD, distribute it to every term. So $12 \times \frac{1}{4}(\frac{1}{3}x + 3)$ becomes $3(\frac{1}{3}x + 3)$ , then distribute again!

What if I get confused with all the fractions?

Break it down step by step: identify all denominators (6, 4, 3), find their LCD (12), then multiply everything by 12. Take your time with each step!

Can I solve this without clearing fractions?

Yes, but it's much harder! You'd have to work with fractions throughout. Clearing fractions first makes the algebra much simpler and reduces calculation errors.

How do I verify my answer with all these fractions?

Substitute x = 17 into the original equation. Calculate each side separately: left side gives $\frac{13}{6}$ , right side also gives $\frac{13}{6}$ . Equal values confirm your answer!

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