Solve for X in (x-4) × 1/2 = 7: Linear Equation Solution

Q: What if the fraction was 1/3 or 1/4 instead?

Use the same method! Multiply both sides by the denominator of the fraction. For $ \frac{1}{3} $, multiply by 3. For $ \frac{1}{4} $, multiply by 4.

Q: Can I solve this by dividing both sides by 1/2?

Yes! Dividing by $ \frac{1}{2} $ is the same as multiplying by 2. Remember: dividing by a fraction means multiplying by its reciprocal.

Q: How do I check if x = 18 is correct?

Substitute back into the original equation: $ (18-4) \times \frac{1}{2} = 14 \times \frac{1}{2} = 7 $. Since this equals 7, our answer is correct!

Q: What if I get a different answer when I check?

If your check doesn't work, go back and review each step. Look for arithmetic errors or places where you didn't apply the same operation to both sides of the equation.

Linear Equations with Fractional Multiplication

$7=(x-4)\times\frac{1}{2}$

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 2 to eliminate the fraction, multiply accordingly

00:11 Open parentheses properly, multiply by each factor

00:17 Arrange the equation so that one side has only the unknown X

00:23 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

$7=(x-4)\times\frac{1}{2}$

How much is X worth?

Step-by-step solution

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

Step 1: Clear the fraction by multiplying both sides of the equation by 2.
Step 2: Isolate $x$ by adding 4 to both sides of the resulting equation.

Now, let's work through each step:
Step 1: Multiply both sides of the equation by 2 to eliminate the fraction:
$7 \times 2 = (x - 4) \times \frac{1}{2} \times 2$

This simplifies to:
$14 = x - 4$

Step 2: Solve for $x$ by adding 4 to both sides:
$14 + 4 = x - 4 + 4$

This simplifies to:
$x = 18$

Therefore, the solution to the equation is $x = 18$ .

Final Answer

$18$

Key Points to Remember

Essential concepts to master this topic

Elimination Rule: Multiply both sides by 2 to clear fractions
Technique: Convert $7 = (x-4) \times \frac{1}{2}$ to $14 = x-4$
Check: Substitute $x = 18$ : $(18-4) \times \frac{1}{2} = 7$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply both sides when clearing fractions
Don't multiply only the right side by 2 and leave 7 unchanged = $7 = x-4$ giving $x = 11$ ! This breaks the equation balance. Always multiply every term on both sides by the same number to maintain equality.

Practice Quiz

Test your knowledge with interactive questions

Determine the value of $$ x $$ :

$$ 2(x+4)+8=0 $$

FAQ

Everything you need to know about this question

Why do we multiply both sides by 2 instead of dividing by 1/2?

Both methods work! Multiplying by 2 is the same as dividing by $\frac{1}{2}$ . Most students find multiplication easier than division with fractions.

What if the fraction was 1/3 or 1/4 instead?

Use the same method! Multiply both sides by the denominator of the fraction. For $\frac{1}{3}$ , multiply by 3. For $\frac{1}{4}$ , multiply by 4.

Can I solve this by dividing both sides by 1/2?

Yes! Dividing by $\frac{1}{2}$ is the same as multiplying by 2. Remember: dividing by a fraction means multiplying by its reciprocal.

How do I check if x = 18 is correct?

Substitute back into the original equation: $(18-4) \times \frac{1}{2} = 14 \times \frac{1}{2} = 7$ . Since this equals 7, our answer is correct!

What if I get a different answer when I check?

If your check doesn't work, go back and review each step. Look for arithmetic errors or places where you didn't apply the same operation to both sides of the equation.

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