Solve for X: (10x-1/5)·1/2 = -1/10+8x Linear Equation

Q: Why do I need to distribute the fraction to both terms?

The distributive property requires you to multiply the outside number by every term inside parentheses. Skipping any term breaks the mathematical rule and gives wrong answers!

Q: Can I work with decimals instead of fractions?

Yes! Convert fractions to decimals: $ \frac{1}{5} = 0.2 $ and $ \frac{1}{10} = 0.1 $. Just be careful with rounding errors in your final answer.

Q: Why do the fraction terms cancel out in this problem?

After distributing, both sides have $ -\frac{1}{10} $, so they subtract to zero. This leaves us with just the x-terms, making the solution cleaner!

Linear Equations with Fraction Distribution

Solve for X:

$(10x-\frac{1}{5})\cdot\frac{1}{2}=-\frac{1}{10}+8x$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 We want to isolate the unknown X

00:07 Open parentheses properly, multiply by each factor

00:23 Divide 10 by 2

00:26 Negative multiplied by positive is always negative

00:37 Let's isolate the unknown X

00:55 Reduce what's possible, collect terms

01:20 Let's isolate the unknown X

01:32 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:

$(10x-\frac{1}{5})\cdot\frac{1}{2}=-\frac{1}{10}+8x$

Step-by-step solution

To solve this problem, we'll proceed step-by-step:

First, we distribute the $\frac{1}{2}$ across the term inside the parentheses:
$\frac{1}{2} \cdot (10x - \frac{1}{5}) = \frac{1}{2} \cdot 10x - \frac{1}{2} \cdot \frac{1}{5}$ .

This simplifies to:
$5x - \frac{1}{10}$ .

Now, our equation becomes:
$5x - \frac{1}{10} = -\frac{1}{10} + 8x$ .

Next, we aim to gather the $x$ terms on one side. Subtract $5x$ from both sides:
$-\frac{1}{10} = -\frac{1}{10} + 8x - 5x$ .

Simplify the right-hand side:
$-\frac{1}{10} = -\frac{1}{10} + 3x$ .

To isolate $3x$ , subtract $-\frac{1}{10}$ from both sides:
$0 = 3x$ .

Divide both sides by 3 to solve for $x$ :
$x = 0$ .

Therefore, the solution to the problem is $x = 0$ .

Final Answer

$0$

Key Points to Remember

Essential concepts to master this topic

Distribution: Multiply each term inside parentheses by outside fraction
Technique: $\frac{1}{2} \cdot 10x = 5x$ and $\frac{1}{2} \cdot \frac{1}{5} = \frac{1}{10}$
Check: Substitute x = 0: $-\frac{1}{10} = -\frac{1}{10} + 8(0)$ gives $-\frac{1}{10} = -\frac{1}{10}$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute the fraction to all terms
Don't multiply $\frac{1}{2}$ by only the first term = wrong coefficients! This leaves the second term unchanged and gives incorrect equations. Always distribute the outside fraction to every single term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

$$ 11=a-16 $$

$a=\text{?}$

FAQ

Everything you need to know about this question

Why do I need to distribute the fraction to both terms?

The distributive property requires you to multiply the outside number by every term inside parentheses. Skipping any term breaks the mathematical rule and gives wrong answers!

How do I multiply fractions like 1/2 × 1/5?

Multiply the numerators together and denominators together: $\frac{1}{2} \times \frac{1}{5} = \frac{1 \times 1}{2 \times 5} = \frac{1}{10}$ . Always simplify if possible!

What if I get x = 0 as my answer?

Zero is a perfectly valid solution! Many equations have x = 0 as the answer. Just make sure to verify by substituting back into the original equation.

Can I work with decimals instead of fractions?

Yes! Convert fractions to decimals: $\frac{1}{5} = 0.2$ and $\frac{1}{10} = 0.1$ . Just be careful with rounding errors in your final answer.

Why do the fraction terms cancel out in this problem?

After distributing, both sides have $-\frac{1}{10}$ , so they subtract to zero. This leaves us with just the x-terms, making the solution cleaner!

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