Solve the Equation: Finding X in (1/2)x + 1 = 1/2

Q: Why do I need to convert 1 to a fraction when subtracting?

You need a common denominator to subtract fractions! Converting 1 to $ \frac{2}{2} $ lets you calculate $ \frac{1}{2} - \frac{2}{2} = -\frac{1}{2} $ easily.

Q: Can I multiply by 2 right at the beginning instead?

Yes! Multiplying the entire equation by 2 first gives you x + 2 = 1, which is easier to solve. Both methods work perfectly!

Q: What if I get a negative answer - is that wrong?

Negative answers are completely normal in algebra! Always check your work by substituting back into the original equation to verify it's correct.

Q: How do I multiply both sides by 2 to eliminate the fraction?

Multiply every term by 2: $ 2 \times \frac{1}{2}x = x $ and $ 2 \times (-\frac{1}{2}) = -1 $. This gives you x = -1.

Q: Why does my teacher want me to show the fraction subtraction step?

It demonstrates you understand fraction operations and don't just guess. Showing $ \frac{1}{2} - \frac{2}{2} = -\frac{1}{2} $ proves you know how to work with fractions properly!

Linear Equations with Fractional Coefficients

Solve for X:

$\frac{1}{2}x+1=\frac{1}{2}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Let's isolate the unknown X

00:16 Let's reduce what we can

00:26 Continue to isolate the unknown X

00:38 Let's reduce what we can

00:49 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:

$\frac{1}{2}x+1=\frac{1}{2}$

Step-by-step solution

To solve the equation $\frac{1}{2}x + 1 = \frac{1}{2}$ , follow these steps:

Step 1: Subtract 1 from both sides of the equation to isolate the term containing $x$ .

$\frac{1}{2}x + 1 - 1 = \frac{1}{2} - 1$

Simplifying the right side, we have:

$\frac{1}{2}x = \frac{1}{2} - 1$
Step 2: Simplify the expression on the right side.

$\frac{1}{2} - 1 = \frac{1}{2} - \frac{2}{2} = -\frac{1}{2}$

So the equation becomes $\frac{1}{2}x = -\frac{1}{2}$ .
Step 3: Solve for $x$ by multiplying both sides of the equation by 2 to eliminate the fraction.

$2 \times \frac{1}{2}x = 2 \times -\frac{1}{2}$

This simplifies to $x = -1$ .

Therefore, the solution to the equation is $x = -1$ .

Final Answer

$-1$

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Remove constant terms first by subtracting from both sides
Technique: Convert $\frac{1}{2} - 1 = \frac{1}{2} - \frac{2}{2} = -\frac{1}{2}$
Check: Substitute x = -1: $\frac{1}{2}(-1) + 1 = \frac{1}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to convert whole numbers to fractions when subtracting
Don't subtract 1 - 1/2 directly = confusion with mixed operations! You need common denominators to subtract fractions properly. Always convert whole numbers like 1 to equivalent fractions (2/2) before subtracting.

Practice Quiz

Test your knowledge with interactive questions

$$ x+7=14 $$

$x=\text{?}$

FAQ

Everything you need to know about this question

Why do I need to convert 1 to a fraction when subtracting?

You need a common denominator to subtract fractions! Converting 1 to $\frac{2}{2}$ lets you calculate $\frac{1}{2} - \frac{2}{2} = -\frac{1}{2}$ easily.

Can I multiply by 2 right at the beginning instead?

Yes! Multiplying the entire equation by 2 first gives you x + 2 = 1, which is easier to solve. Both methods work perfectly!

What if I get a negative answer - is that wrong?

Negative answers are completely normal in algebra! Always check your work by substituting back into the original equation to verify it's correct.

How do I multiply both sides by 2 to eliminate the fraction?

Multiply every term by 2: $2 \times \frac{1}{2}x = x$ and $2 \times (-\frac{1}{2}) = -1$ . This gives you x = -1.

Why does my teacher want me to show the fraction subtraction step?

It demonstrates you understand fraction operations and don't just guess. Showing $\frac{1}{2} - \frac{2}{2} = -\frac{1}{2}$ proves you know how to work with fractions properly!

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