Solve the Equation: (x-3) × 1/2 = 2 Step by Step

Q: Why do I multiply by 2 instead of dividing by 1/2?

Great question! Multiplying by 2 and dividing by $ \frac{1}{2} $ are the same operation. Since $ \frac{1}{2} $ is the reciprocal of 2, multiplying by 2 is often easier to visualize.

Q: What if I solve (x-3) first before dealing with the fraction?

Don't do that! You can't separate (x-3) from the multiplication. The fraction $ \frac{1}{2} $ multiplies the entire expression (x-3), so clear the fraction first.

Q: Can I move the fraction to the other side instead?

Yes! You could rewrite as $ \frac{2}{\frac{1}{2}} = x-3 $, which gives 4 = x-3. However, multiplying both sides by 2 is usually simpler and less confusing.

Q: How do I check my answer when there's a fraction involved?

Substitute x = 7 into the original equation: (7-3) × $ \frac{1}{2} $ = 4 × $ \frac{1}{2} $ = 2. Since this equals 2, your answer is correct!

Q: What if I get confused about which side to multiply?

Always multiply BOTH sides by the same number. If you see a fraction anywhere in the equation, multiply every single term on both sides to maintain the equality.

Linear Equations with Fractional Coefficients

$2=(x-3)\times\frac{1}{2}$

How much is Xworth?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's multiply by the denominator to eliminate the fraction, we'll multiply accordingly

00:14 Let's 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

$2=(x-3)\times\frac{1}{2}$

How much is Xworth?

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 2.
Step 2: Simplify the resulting equation.
Step 3: Solve for $x$ by adding 3 to both sides.

Now, let's work through each step:
Step 1: Starting with the equation $2 = (x-3) \times \frac{1}{2}$ , we multiply both sides by 2 to get rid of the fraction:
$2 \times 2 = (x-3) \times \frac{1}{2} \times 2$

This simplifies to:
$4 = x - 3$

Step 2: Next, we solve for $x$ by adding 3 to both sides:
$4 + 3 = x$

Therefore, $x = 7$ .

Therefore, the solution to the problem is $x = 7$ .

Final Answer

$7$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both sides by reciprocal to eliminate fractions
Technique: Multiply by 2 to clear $\frac{1}{2}$ : 2 × 2 = 4
Check: Substitute x = 7: (7-3) × $\frac{1}{2}$ = 2 ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting to eliminate fractions
Don't try to add 3 to both sides when you see (x-3) × $\frac{1}{2}$ = wrong approach! This doesn't eliminate the fraction and creates a mess. Always multiply both sides by the reciprocal or denominator to clear fractions first.

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 do I multiply by 2 instead of dividing by 1/2?

Great question! Multiplying by 2 and dividing by $\frac{1}{2}$ are the same operation. Since $\frac{1}{2}$ is the reciprocal of 2, multiplying by 2 is often easier to visualize.

What if I solve (x-3) first before dealing with the fraction?

Don't do that! You can't separate (x-3) from the multiplication. The fraction $\frac{1}{2}$ multiplies the entire expression (x-3), so clear the fraction first.

Can I move the fraction to the other side instead?

Yes! You could rewrite as $\frac{2}{\frac{1}{2}} = x-3$ , which gives 4 = x-3. However, multiplying both sides by 2 is usually simpler and less confusing.

How do I check my answer when there's a fraction involved?

Substitute x = 7 into the original equation: (7-3) × $\frac{1}{2}$ = 4 × $\frac{1}{2}$ = 2. Since this equals 2, your answer is correct!

What if I get confused about which side to multiply?

Always multiply BOTH sides by the same number. If you see a fraction anywhere in the equation, multiply every single term on both sides to maintain the equality.

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