Solve for X in the Fraction Equation: (8x-4)/5 = (2x+2)/4

Q: When can I use cross-multiplication?

Cross-multiplication works when you have one fraction equals another fraction, like $ \frac{a}{b} = \frac{c}{d} $. This lets you write ad = bc directly.

Q: Why do I get such a messy fraction answer?

Fractional answers like $ \frac{26}{22} $ are normal! You can simplify by finding the GCD of 26 and 22, which is 2, giving $ \frac{13}{11} $.

Q: Do I need to check if 26 and 22 have common factors?

Yes! Always simplify fractions to lowest terms. Since both 26 and 22 are divisible by 2, the simplified answer is $ \frac{13}{11} $.

Q: What if I made an algebra mistake after cross-multiplying?

Common errors include sign mistakes when moving terms or forgetting to distribute. Always check each step: expand parentheses carefully, then combine like terms systematically.

Q: How do I verify this fractional answer?

Substitute $ x = \frac{26}{22} $ into both sides of the original equation. Calculate each side separately - they should both equal $ \frac{13}{11} $!

Cross-Multiplication with Fractional Equations

Solve for x:

$\frac{8x-4}{5}=\frac{2x+2}{4}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to isolate the unknown X

00:07 We'll multiply by both denominators to eliminate fractions

00:16 We'll properly open parentheses, multiply by each factor

00:28 We'll arrange the equation so that one side has only the unknown X

00:50 We'll isolate the unknown X

00:58 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for x:

$\frac{8x-4}{5}=\frac{2x+2}{4}$

Step-by-step solution

To get rid of the fraction mechanics, we will cross multiply between the sides:

$4(8x-4)=5(2x+2)$

We expand the parentheses by multiplying the outer element by each of the elements inside the parentheses:

$32x-16=10x+10$

We arrange the sides accordingly so that the elements with the X are on the left side and those without the X are on the right side:

$32x-10x=10+16$

We calculate the elements:

$22x=26$

We divide the two sections by 22:

$\frac{22x}{22}=\frac{26}{22}$

$x=\frac{26}{22}$

Final Answer

$\frac{26}{22}$

Key Points to Remember

Essential concepts to master this topic

Cross-Multiplication: When equation equals two fractions, multiply diagonally across
Distribution: Expand 4(8x-4) = 32x-16 and 5(2x+2) = 10x+10
Verification: Substitute x = 26/22 back: both sides equal 13/11 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute after cross-multiplying
Don't write 4(8x-4) = 32x-4 by only multiplying the first term = incomplete expansion! This gives wrong coefficients and wrong solutions. Always distribute the outside number to every term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

When can I use cross-multiplication?

Cross-multiplication works when you have one fraction equals another fraction, like $\frac{a}{b} = \frac{c}{d}$ . This lets you write ad = bc directly.

Why do I get such a messy fraction answer?

Fractional answers like $\frac{26}{22}$ are normal! You can simplify by finding the GCD of 26 and 22, which is 2, giving $\frac{13}{11}$ .

Do I need to check if 26 and 22 have common factors?

Yes! Always simplify fractions to lowest terms. Since both 26 and 22 are divisible by 2, the simplified answer is $\frac{13}{11}$ .

What if I made an algebra mistake after cross-multiplying?

Common errors include sign mistakes when moving terms or forgetting to distribute. Always check each step: expand parentheses carefully, then combine like terms systematically.

How do I verify this fractional answer?

Substitute $x = \frac{26}{22}$ into both sides of the original equation. Calculate each side separately - they should both equal $\frac{13}{11}$ !

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