Solve for X: Finding the Value in x/4 = 3

Q: Why do I multiply by 4 instead of dividing by 4?

When you have $ \frac{x}{4} = 3 $, the variable x is being divided by 4. To undo division, you need to multiply by 4. Think of it as the opposite operation!

Q: What happens to the 4 in the denominator after multiplying?

When you multiply $ \frac{x}{4} $ by 4, the 4s cancel out: $ 4 \times \frac{x}{4} = \frac{4x}{4} = x $. This leaves you with just x on the left side!

Q: Can I solve this by cross-multiplying?

Not directly! Cross-multiplication works when you have two fractions equal to each other. Here you have a fraction equal to a whole number, so multiply both sides by the denominator instead.

Q: How do I check if x = 12 is correct?

Substitute 12 for x in the original equation: $ \frac{12}{4} = 3 $. Since $ \frac{12}{4} = 3 $ and $ 3 = 3 $, your answer is correct!

Q: What if the denominator was a different number?

The process stays the same! If you had $ \frac{x}{7} = 5 $, you would multiply both sides by 7 to get $ x = 35 $. Always multiply by whatever number is in the denominator.

Linear Equations with Fraction Isolation

Solve for X:

$\frac{x}{4}=3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to isolate the unknown X

00:07 Let's arrange the equation so that one side has only the unknown X

00:11 Multiply by the denominator to eliminate the fraction

00:16 Simplify what we can

00:21 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:

$\frac{x}{4}=3$

Step-by-step solution

We use the formula:

$a\cdot x=b$

$x=\frac{b}{a}$

We multiply the numerator by X and write the exercise as follows:

$\frac{x}{4}=3$

We multiply by 4 to get rid of the fraction's denominator:

$4\times\frac{x}{4}=3\times4$

Then, we remove the common factor from the left side and perform the multiplication on right side to obtain:

$x=12$

Final Answer

$12$

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: $4 \times \frac{x}{4} = 4 \times 3$
Check: Substitute x = 12 back into original: $\frac{12}{4} = 3$ ✓

Common Mistakes

Avoid these frequent errors

Dividing instead of multiplying to eliminate the fraction
Don't divide both sides by 4 when you see x/4 = 3 = x/16! This makes the fraction worse, not better. Always multiply both sides by the denominator to eliminate fractions completely.

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 multiply by 4 instead of dividing by 4?

When you have $\frac{x}{4} = 3$ , the variable x is being divided by 4. To undo division, you need to multiply by 4. Think of it as the opposite operation!

What happens to the 4 in the denominator after multiplying?

When you multiply $\frac{x}{4}$ by 4, the 4s cancel out: $4 \times \frac{x}{4} = \frac{4x}{4} = x$ . This leaves you with just x on the left side!

Can I solve this by cross-multiplying?

Not directly! Cross-multiplication works when you have two fractions equal to each other. Here you have a fraction equal to a whole number, so multiply both sides by the denominator instead.

How do I check if x = 12 is correct?

Substitute 12 for x in the original equation: $\frac{12}{4} = 3$ . Since $\frac{12}{4} = 3$ and $3 = 3$ , your answer is correct!

What if the denominator was a different number?

The process stays the same! If you had $\frac{x}{7} = 5$ , you would multiply both sides by 7 to get $x = 35$ . Always multiply by whatever number is in the denominator.

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