Solve the Fraction Equation: Unraveling X in (1/4)(x - 8) = 1

Q: Why multiply by 4 instead of dividing by 1/4?

Both methods work, but multiplying by 4 is easier! Dividing by a fraction means multiplying by its reciprocal (4), so you end up doing the same thing anyway.

Q: What if the fraction coefficient was something like 2/3?

Same process! Multiply both sides by the denominator (3). So $ \frac{2}{3}(x-8) = 1 $ becomes $ 2(x-8) = 3 $ after multiplying by 3.

Q: Can I solve this by distributing the fraction first?

You can, but it's harder! You'd get $ \frac{x}{4} - 2 = 1 $, then need to work with fractions longer. Clearing fractions first keeps everything simpler.

Q: How do I check my answer quickly?

Substitute back into the original equation: $ \frac{1}{4}(12-8) = \frac{1}{4} \times 4 = 1 $. If both sides equal 1, you're correct!

Q: What if I get a negative answer?

Negative answers are totally normal! Just make sure to check your arithmetic and substitute back to verify. Don't assume a negative result is wrong.

Linear Equations with Fractional Coefficients

Solve for X:

$\frac{1}{4}(x-8)=1$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Multiply by 4 to eliminate the fraction

00:13 Arrange the equation so that one side has only the unknown X

00:19 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:

$\frac{1}{4}(x-8)=1$

Step-by-step solution

To solve this problem, we will follow these steps:

Step 1: Multiply both sides of the equation by 4 to eliminate the fraction.
Step 2: Simplify the resulting equation.
Step 3: Solve for $x$ .

Let's work through these steps:

Step 1: Start with the equation:

$\frac{1}{4}(x - 8) = 1$

Multiply both sides by 4 to remove the fraction:

$4 \times \frac{1}{4}(x - 8) = 4 \times 1$

This simplifies to:

$x - 8 = 4$

Step 2: To isolate $x$ , add 8 to both sides of the equation:

$x - 8 + 8 = 4 + 8$

This results in:

$x = 12$

Therefore, the solution to the equation is $x = 12$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both sides by the denominator to eliminate fractions
Technique: Multiply both sides by 4: $4 \times \frac{1}{4}(x-8) = 4 \times 1$
Check: Substitute x = 12: $\frac{1}{4}(12-8) = \frac{1}{4}(4) = 1$ ✓

Common Mistakes

Avoid these frequent errors

Distributing before clearing the fraction
Don't distribute $\frac{1}{4}$ to get $\frac{x}{4} - 2 = 1$ first = more complex fractions! This makes the problem harder and increases error chances. Always multiply both sides by the denominator first to eliminate fractions completely.

Practice Quiz

Test your knowledge with interactive questions

$$ 5x=0 $$

FAQ

Everything you need to know about this question

Why multiply by 4 instead of dividing by 1/4?

Both methods work, but multiplying by 4 is easier! Dividing by a fraction means multiplying by its reciprocal (4), so you end up doing the same thing anyway.

What if the fraction coefficient was something like 2/3?

Same process! Multiply both sides by the denominator (3). So $\frac{2}{3}(x-8) = 1$ becomes $2(x-8) = 3$ after multiplying by 3.

Can I solve this by distributing the fraction first?

You can, but it's harder! You'd get $\frac{x}{4} - 2 = 1$ , then need to work with fractions longer. Clearing fractions first keeps everything simpler.

How do I check my answer quickly?

Substitute back into the original equation: $\frac{1}{4}(12-8) = \frac{1}{4} \times 4 = 1$ . If both sides equal 1, you're correct!

What if I get a negative answer?

Negative answers are totally normal! Just make sure to check your arithmetic and substitute back to verify. Don't assume a negative result is wrong.

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