Solve for X in 2=(x-2)×1/4: Step-by-Step Solution

Q: Why multiply both sides by 4 instead of dividing?

Multiplying by 4 is the opposite operation of multiplying by $ \frac{1}{4} $! Since $ 4 \times \frac{1}{4} = 1 $, this eliminates the fraction completely and makes solving much easier.

Q: Can I distribute the multiplication first?

You could, but it's more complicated! You'd get $ 2 = \frac{x}{4} - \frac{2}{4} $, then still need to clear fractions. It's easier to multiply both sides by 4 right away.

Q: What if I forget to multiply both sides?

You'll get a wrong answer! For example, if you only multiply the right side by 4, you'd get $ 2 = x - 2 $, so x = 4. But checking: $ (4-2) \times \frac{1}{4} = \frac{1}{2} \neq 2 $.

Q: Is x = 10 the only solution?

Yes! Linear equations like this one have exactly one solution. You can verify this by substituting: $ 2 = (10-2) \times \frac{1}{4} = 8 \times \frac{1}{4} = 2 $ ✓

Linear Equations with Fractional Multiplication

$2=(x-2)\times\frac{1}{4}$

How much is X worth?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Multiply by the denominator to eliminate the fraction, multiply accordingly

00:08 Open the parentheses properly, multiply by each factor

00:16 Arrange the equation so that only the unknown X is on one side

00:22 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

$2=(x-2)\times\frac{1}{4}$

How much is X worth?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Eliminate the fraction by multiplying both sides of the equation by 4.
Step 2: Simplify and solve for $x$ .

Let's work through each step:

Step 1: The original equation is $2 = (x-2) \times \frac{1}{4}$ .
To eliminate the fraction, multiply both sides by 4:
$4 \times 2 = 4 \times (x-2) \times \frac{1}{4}$

This simplifies to:
$8 = x - 2$

Step 2: Solve for $x$ .
Add 2 to both sides to isolate $x$ :
$8 + 2 = x$

This simplifies to:
$x = 10$

Therefore, the solution to the problem is $x = 10$ .

Final Answer

$10$

Key Points to Remember

Essential concepts to master this topic

Elimination: Multiply both sides by 4 to clear the fraction
Technique: $4 \times 2 = 4 \times (x-2) \times \frac{1}{4}$ becomes 8 = x - 2
Check: Substitute x = 10 back: $(10-2) \times \frac{1}{4} = 2$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying only the right side by 4
Don't multiply just $(x-2) \times \frac{1}{4}$ by 4 and leave 2 unchanged = unbalanced equation! This breaks the equality because you must do the same operation to both sides. Always multiply both sides by the same number to maintain balance.

Practice Quiz

Test your knowledge with interactive questions

$$ 5x=1 $$

What is the value of x?

FAQ

Everything you need to know about this question

Why multiply both sides by 4 instead of dividing?

Multiplying by 4 is the opposite operation of multiplying by $\frac{1}{4}$ ! Since $4 \times \frac{1}{4} = 1$ , this eliminates the fraction completely and makes solving much easier.

Can I distribute the multiplication first?

You could, but it's more complicated! You'd get $2 = \frac{x}{4} - \frac{2}{4}$ , then still need to clear fractions. It's easier to multiply both sides by 4 right away.

What if I forget to multiply both sides?

You'll get a wrong answer! For example, if you only multiply the right side by 4, you'd get $2 = x - 2$ , so x = 4. But checking: $(4-2) \times \frac{1}{4} = \frac{1}{2} \neq 2$ .

How do I know when to multiply to eliminate fractions?

Look for fractions in your equation! When you see terms like $\times \frac{1}{4}$ or $\frac{x}{3}$ , multiplying by the denominator will clear the fraction and simplify your work.

Is x = 10 the only solution?

Yes! Linear equations like this one have exactly one solution. You can verify this by substituting: $2 = (10-2) \times \frac{1}{4} = 8 \times \frac{1}{4} = 2$ ✓

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