Solve for X: -1/8x + 4 = 7x - 4/5 Linear Equation

Q: Why can't I just work with decimals instead of fractions?

You can convert to decimals, but fractions often give exact answers. Converting $ \frac{1}{8} $ to 0.125 might lead to rounding errors in your final answer.

Q: How do I add 7x and 1/8x together?

Convert 7 to eighths first: $ 7 = \frac{56}{8} $. Then $ 7x + \frac{1}{8}x = \frac{56}{8}x + \frac{1}{8}x = \frac{57}{8}x $.

Q: Should I simplify the final fraction 192/285?

Check if it can be simplified by finding the GCD of 192 and 285. If they share common factors, divide both numerator and denominator by the GCD.

Q: What if I move the x-terms to the left side instead?

That works too! You'd get $ -\frac{57}{8}x = -\frac{24}{5} $, then divide by $ -\frac{57}{8} $ to get the same answer.

Q: How do I multiply by a reciprocal like 8/57?

Dividing by a fraction is the same as multiplying by its reciprocal. So $ \frac{24}{5} \div \frac{57}{8} = \frac{24}{5} \times \frac{8}{57} = \frac{192}{285} $.

Linear Equations with Mixed Fractions

Solve for X:

$-\frac{1}{8}x+4=7x-\frac{4}{5}$

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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

00:37 We will reduce what we can

00:59 We will group terms

01:09 We will convert numbers and fractions to improper fractions

01:15 We will multiply by the reciprocal fraction to isolate X

01:35 We will carefully multiply numerator by numerator and denominator by denominator

01:42 We will reduce what we can

01:45 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:

$-\frac{1}{8}x+4=7x-\frac{4}{5}$

Step-by-step solution

To solve the equation $-\frac{1}{8}x + 4 = 7x - \frac{4}{5}$ , follow these steps:

Step 1: Move the $x$ terms to one side of the equation.
Add $\frac{1}{8}x$ to both sides:

$-\frac{1}{8}x + \frac{1}{8}x + 4 = 7x + \frac{1}{8}x - \frac{4}{5} \\ 4 = 7x + \frac{1}{8}x - \frac{4}{5}$

Step 2: Simplify by combining like terms. Combine $x$ -terms on the right:

$4 = \left(7 + \frac{1}{8}\right)x - \frac{4}{5}$

Step 3: Express $7 + \frac{1}{8}$ as a single fraction: $\frac{56}{8} + \frac{1}{8} = \frac{57}{8}$ .

Step 4: Substitute back:

$4 = \frac{57}{8}x - \frac{4}{5}$

Step 5: Move the constant term to the other side. Add $\frac{4}{5}$ to both sides:

$4 + \frac{4}{5} = \frac{57}{8}x \\ \frac{20}{5} + \frac{4}{5} = \frac{57}{8}x \\ \frac{24}{5} = \frac{57}{8}x$

Step 6: Solve for $x$ by dividing both sides by $\frac{57}{8}$ (multiply by $\frac{8}{57}$ ):

$x= \frac{24}{5} \times \frac{8}{57} \\ x = \frac{192}{285}$

Therefore, the solution to the problem is $x = \frac{192}{285}$ .

Final Answer

$\frac{192}{285}$

Key Points to Remember

Essential concepts to master this topic

Strategy: Collect all x-terms on one side, constants on other
Technique: Convert $7 + \frac{1}{8} = \frac{56}{8} + \frac{1}{8} = \frac{57}{8}$
Check: Substitute $x = \frac{192}{285}$ back into original equation ✓

Common Mistakes

Avoid these frequent errors

Incorrectly combining x-terms with different coefficients
Don't add 7x and 1/8x without converting to common denominators = wrong coefficient! This gives an incorrect final answer. Always convert to common fractions first: 7 = 56/8, so 7x + 1/8x = 57/8x.

Practice Quiz

Test your knowledge with interactive questions

$$ x+7=14 $$

$x=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just work with decimals instead of fractions?

You can convert to decimals, but fractions often give exact answers. Converting $\frac{1}{8}$ to 0.125 might lead to rounding errors in your final answer.

How do I add 7x and 1/8x together?

Convert 7 to eighths first: $7 = \frac{56}{8}$ . Then $7x + \frac{1}{8}x = \frac{56}{8}x + \frac{1}{8}x = \frac{57}{8}x$ .

Should I simplify the final fraction 192/285?

Check if it can be simplified by finding the GCD of 192 and 285. If they share common factors, divide both numerator and denominator by the GCD.

What if I move the x-terms to the left side instead?

That works too! You'd get $-\frac{57}{8}x = -\frac{24}{5}$ , then divide by $-\frac{57}{8}$ to get the same answer.

How do I multiply by a reciprocal like 8/57?

Dividing by a fraction is the same as multiplying by its reciprocal. So $\frac{24}{5} \div \frac{57}{8} = \frac{24}{5} \times \frac{8}{57} = \frac{192}{285}$ .

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