Solve the Fraction Equation: (x-5)/7 = 2/11

Q: Why can I cross-multiply with this equation?

Cross-multiplication works because you have one fraction equal to another fraction. When $ \frac{x-5}{7} = \frac{2}{11} $, you can multiply both sides by both denominators to eliminate fractions.

Q: What if I get confused with the cross-multiplication setup?

Think of it as: left numerator × right denominator = right numerator × left denominator. So $ (x-5) \times 11 = 2 \times 7 $.

Q: Do I need to simplify my final fraction answer?

$ \frac{69}{11} $ is already in simplest form since 69 and 11 share no common factors other than 1. You can also convert it to a mixed number: $ 6\frac{3}{11} $.

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

Substitute your answer back into the original equation. If $ x = \frac{69}{11} $, then $ \frac{\frac{69}{11}-5}{7} $ should equal $ \frac{2}{11} $.

Cross-Multiplication with Rational Equations

Solve for X:

$\frac{x-5}{7}=\frac{2}{11}$

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Step-by-step video solution

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00:00 Solution

00:03 We want to isolate the unknown X

00:07 Multiply by both denominators to eliminate fractions

00:20 Open parentheses properly, multiply by each factor

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

00:50 Isolate the unknown X

00:57 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:

$\frac{x-5}{7}=\frac{2}{11}$

Step-by-step solution

To solve $\frac{x-5}{7} = \frac{2}{11}$ , we will use cross-multiplication:

Step 1: Cross-multiply the equation: $(x-5) \times 11 = 7 \times 2$ .
Step 2: Simplify both sides: $11(x - 5) = 14$ .
Step 3: Distribute the 11 on the left side: $11x - 55 = 14$ .
Step 4: Add 55 to both sides to isolate the $11x$ term: $11x = 14 + 55$ .
Step 5: Calculate the right side: $11x = 69$ .
Step 6: Divide both sides by 11 to solve for $x$ : $x = \frac{69}{11}$ .

Therefore, the solution to the problem is $x = \frac{69}{11}$ , which matches the first answer choice provided.

Final Answer

$\frac{69}{11}$

Key Points to Remember

Essential concepts to master this topic

Cross-Multiplication Rule: When $\frac{a}{b} = \frac{c}{d}$ , then $a \times d = b \times c$
Distribution Technique: $11(x-5) = 11x - 55$ distributes the 11
Verification Check: Substitute $x = \frac{69}{11}$ back: $\frac{\frac{69}{11}-5}{7} = \frac{2}{11}$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute when expanding parentheses
Don't write 11(x-5) = 11x - 5 = wrong answer! This skips distributing 11 to both terms inside parentheses. Always distribute: 11(x-5) = 11x - 55.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why can I cross-multiply with this equation?

Cross-multiplication works because you have one fraction equal to another fraction. When $\frac{x-5}{7} = \frac{2}{11}$ , you can multiply both sides by both denominators to eliminate fractions.

What if I get confused with the cross-multiplication setup?

Think of it as: left numerator × right denominator = right numerator × left denominator. So $(x-5) \times 11 = 2 \times 7$ .

Do I need to simplify my final fraction answer?

$\frac{69}{11}$ is already in simplest form since 69 and 11 share no common factors other than 1. You can also convert it to a mixed number: $6\frac{3}{11}$ .

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

Substitute your answer back into the original equation. If $x = \frac{69}{11}$ , then $\frac{\frac{69}{11}-5}{7}$ should equal $\frac{2}{11}$ .

Can I solve this equation a different way?

Yes! You could multiply both sides by 7, then by 11 to clear fractions step by step. But cross-multiplication is faster when you have this fraction = fraction format.

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