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

Find the value of the parameter X

$\frac{1}{3}x=\frac{1}{9}$

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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