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

Find the value of the parameter X

$\frac{1}{3}x=\frac{1}{9}$

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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