Solve for X: Fraction Equation 4/(x+5) = 8/((2-x)×3)

Q: When can I use cross-multiplication?

Cross-multiplication works when you have exactly one fraction on each side of the equation. Like $ \frac{a}{b} = \frac{c}{d} $, then $ a \times d = b \times c $.

Q: Why do I get negative answers sometimes?

Negative solutions are completely normal! In this problem, $ x = -\frac{4}{5} $ makes perfect sense. Always check that your answer doesn't make any denominator equal to zero.

Q: How do I handle the multiplication in the denominator?

Treat $ (2-x) \times 3 $ as a single unit when cross-multiplying. So $ \frac{8}{(2-x) \times 3} $ becomes $ \frac{8}{3(2-x)} $.

Q: What if my final fraction doesn't simplify nicely?

That's okay! Always reduce to lowest terms. Here, $ -\frac{16}{20} = -\frac{4}{5} $ by dividing both numerator and denominator by 4.

Q: Should I check for restricted values?

Yes! Make sure $ x + 5 ≠ 0 $ and $ 2 - x ≠ 0 $. So $ x ≠ -5 $ and $ x ≠ 2 $. Our answer $ -\frac{4}{5} $ is safe!

Rational Equations with Cross-Multiplication

Solve for X:

$\frac{4}{x+5}=\frac{8}{(2-x)\times3}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Multiply by common denominator to eliminate fractions

00:21 Carefully open parentheses properly, multiply by each factor

00:46 Arrange the equation so that X is isolated on one side

01:03 Combine like terms

01:10 Isolate X

01:14 Factor 16 into 4 and 4

01:21 Factor 20 into 5 and 4

01:27 Simplify as much as possible

01:32 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:

$\frac{4}{x+5}=\frac{8}{(2-x)\times3}$

Step-by-step solution

To solve the equation $\frac{4}{x+5} = \frac{8}{(2-x) \times 3}$ , we will use cross-multiplication.

Step 1: Set up the cross-multiplication: $4 \times (2-x) \times 3 = 8 \times (x+5)$
Step 2: Simplify the left side of the equation: $12(2-x) = 8(x+5)$
Step 3: Distribute on both sides: $24 - 12x = 8x + 40$
Step 4: Combine like terms. First, bring all terms involving $x$ to one side and constant terms to the other side: $24 - 40 = 8x + 12x$
Step 5: Simplify the equation: $-16 = 20x$
Step 6: Solve for $x$ by dividing both sides by 20: $x = -\frac{16}{20}$
Step 7: Simplify the fraction: $x = -\frac{4}{5}$

Therefore, the solution to the equation is $x = -\frac{4}{5}$ .

Final Answer

$-\frac{4}{5}$

Key Points to Remember

Essential concepts to master this topic

Cross-Multiplication Rule: When two fractions are equal, cross multiply to solve
Distribution Technique: $4 \times 3(2-x) = 12(2-x) = 24-12x$
Verification Check: Substitute $x = -\frac{4}{5}$ back into original equation ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute after cross-multiplying
Don't leave $4 \times 3(2-x)$ as $12(2-x)$ without distributing = missing the negative term! This leads to incorrect combining of like terms. Always distribute completely: $12(2-x) = 24 - 12x$ .

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 6 - x = 10 - 2 $$

FAQ

Everything you need to know about this question

When can I use cross-multiplication?

Cross-multiplication works when you have exactly one fraction on each side of the equation. Like $\frac{a}{b} = \frac{c}{d}$ , then $a \times d = b \times c$ .

Why do I get negative answers sometimes?

Negative solutions are completely normal! In this problem, $x = -\frac{4}{5}$ makes perfect sense. Always check that your answer doesn't make any denominator equal to zero.

How do I handle the multiplication in the denominator?

Treat $(2-x) \times 3$ as a single unit when cross-multiplying. So $\frac{8}{(2-x) \times 3}$ becomes $\frac{8}{3(2-x)}$ .

What if my final fraction doesn't simplify nicely?

That's okay! Always reduce to lowest terms. Here, $-\frac{16}{20} = -\frac{4}{5}$ by dividing both numerator and denominator by 4.

Should I check for restricted values?

Yes! Make sure $x + 5 ≠ 0$ and $2 - x ≠ 0$ . So $x ≠ -5$ and $x ≠ 2$ . Our answer $-\frac{4}{5}$ is safe!

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Solve for X: Fraction Equation 4/(x+5) = 8/((2-x)×3)

Rational Equations with Cross-Multiplication

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

When can I use cross-multiplication?

Why do I get negative answers sometimes?

How do I handle the multiplication in the denominator?

What if my final fraction doesn't simplify nicely?

Should I check for restricted values?

🌟 Unlock Your Math Potential

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