Solve the Linear Fraction Equation: (5-x)/8 = (3+x)/2

Q: When can I use cross-multiplication?

Cross-multiplication works perfectly when you have one fraction on each side of the equals sign! This is exactly what we have: $ \frac{5-x}{8} = \frac{3+x}{2} $.

Q: Why do I get a negative fraction as my answer?

Negative answers are completely normal! The value $ x = \frac{-14}{10} $ means x is negative, which makes sense when you substitute it back into the original equation.

Q: Should I simplify the fraction answer?

It depends on the question format! $ \frac{-14}{10} $ can be simplified to $ -\frac{7}{5} $, but both forms are mathematically correct. Check what format your answer choices use.

Q: How do I check if my cross-multiplication was correct?

After cross-multiplying, make sure you have: left fraction's numerator × right fraction's denominator = right fraction's numerator × left fraction's denominator. So (5-x) × 2 should equal (3+x) × 8.

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

Take your time with the distribution and combining like terms! Write each step clearly: expand parentheses first, then collect all x-terms on one side and constants on the other.

Linear Equations with Cross-Multiplication Method

Solve for X:

$\frac{5-x}{8}=\frac{3+x}{2}$

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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 Multiply by the denominator to eliminate fractions

00:15 Simplify as much as possible

00:21 Divide 8 by 2

00:26 Open parentheses properly, multiply by each factor

00:35 Arrange the equation so that one side has only the unknown X

00:53 Isolate the unknown X

01:02 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:

$\frac{5-x}{8}=\frac{3+x}{2}$

Step-by-step solution

To solve the equation $\frac{5-x}{8} = \frac{3+x}{2}$ , we will follow these steps:

Step 1: Eliminate the fractions by cross-multiplying.
Step 2: Simplify the resulting equation.
Step 3: Solve for $x$ .

Let's proceed with each step:

Step 1: Cross-multiply.
Cross-multiplying gives:

$(5 - x) \times 2 = (3 + x) \times 8$

Which simplifies to:

$2(5 - x) = 8(3 + x)$

Step 2: Expand and simplify.
Distribute the constants inside the parentheses:

$10 - 2x = 24 + 8x$

Step 3: Isolate $x$ .
Add $2x$ to both sides to bring all terms involving $x$ to one side:

$10 = 24 + 10x$

Subtract 24 from both sides to isolate the term with $x$ :

$10 - 24 = 10x$

Simplify:

$-14 = 10x$

Finally, divide both sides by 10 to solve for $x$ :

$x = \frac{-14}{10}$

Therefore, the solution to the problem is $x = \frac{-14}{10}$ , which corresponds to choice .

Final Answer

$\frac{-14}{10}$

Key Points to Remember

Essential concepts to master this topic

Cross-Multiply: Multiply diagonally to eliminate fractions completely
Technique: Transform $\frac{5-x}{8} = \frac{3+x}{2}$ into $2(5-x) = 8(3+x)$
Check: Substitute $x = \frac{-14}{10}$ back: both sides equal $\frac{19}{5}$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute after cross-multiplication
Don't write 2(5-x) = 8(3+x) and jump to 10-x = 24+x! This skips the distribution step and gives wrong coefficients. Always distribute first: 2(5-x) becomes 10-2x, and 8(3+x) becomes 24+8x.

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 perfectly when you have one fraction on each side of the equals sign! This is exactly what we have: $\frac{5-x}{8} = \frac{3+x}{2}$ .

Why do I get a negative fraction as my answer?

Negative answers are completely normal! The value $x = \frac{-14}{10}$ means x is negative, which makes sense when you substitute it back into the original equation.

Should I simplify the fraction answer?

It depends on the question format! $\frac{-14}{10}$ can be simplified to $-\frac{7}{5}$ , but both forms are mathematically correct. Check what format your answer choices use.

How do I check if my cross-multiplication was correct?

After cross-multiplying, make sure you have: left fraction's numerator × right fraction's denominator = right fraction's numerator × left fraction's denominator. So (5-x) × 2 should equal (3+x) × 8.

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

Take your time with the distribution and combining like terms! Write each step clearly: expand parentheses first, then collect all x-terms on one side and constants on the other.

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