Solve the Rational Equation: Finding X in (6+x)/(x+5) = 4/11

Q: Why can't I just multiply both sides by (x+5)?

You could, but cross-multiplication is more efficient when you have one fraction equal to another fraction. It eliminates both denominators in one step!

Q: How do I handle the decimal answer -6.57?

The exact answer is $ \frac{-46}{7} $. You can leave it as a fraction or convert to decimal. Both forms are correct, but fractions are often preferred for exact values.

Q: Can I check my work without substituting back?

Substitution is the best verification method, but you can also check your algebra steps. Make sure your cross-multiplication and distribution are correct at each step.

Q: What if I get a positive answer instead?

Double-check your signs! When you get $ 7x = -46 $, dividing by positive 7 gives a negative result. Sign errors are very common in multi-step problems.

Cross-Multiplication with Rational Equations

Solve for X:

$\frac{6+x}{x+5}=\frac{4}{11}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:05 Multiply by denominators to eliminate fractions

00:21 Simplify as much as possible

00:36 Carefully open parentheses properly, multiply by each term

00:51 Arrange the equation so that X is isolated on one side

01:08 Combine like terms

01:20 Isolate X

01:31 Simplify as much as possible

01:34 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:

$\frac{6+x}{x+5}=\frac{4}{11}$

Step-by-step solution

To solve the given equation $\frac{6+x}{x+5}=\frac{4}{11}$ , follow these steps:

Step 1: Use cross-multiplication to eliminate the fractions. Multiply $11(6 + x)$ and $4(x + 5)$ across the equation:

$11(6 + x) = 4(x + 5)$

Step 2: Expand both sides of the equation:

$66 + 11x = 4x + 20$

Step 3: Isolate $x$ by first eliminating the smaller $x$ term. Subtract $4x$ from both sides:

$66 + 11x - 4x = 20$

$66 + 7x = 20$

Step 4: Further simplify to isolate $x$ . Subtract 66 from both sides:

$7x = 20 - 66$

$7x = -46$

Step 5: Solve for $x$ by dividing both sides by 7:

$x = \frac{-46}{7}$

$x = -6.57$

Therefore, the solution to the equation is $\textbf{$ x = -6.57 } $$ .

Final Answer

$-6.57$

Key Points to Remember

Essential concepts to master this topic

Cross-Multiplication Rule: Set products of diagonals equal: (6+x)(11) = 4(x+5)
Distribution Technique: Expand to 66 + 11x = 4x + 20 carefully
Verification Check: Substitute x = -46/7 back into original equation both sides equal ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute after cross-multiplication
Don't write 11(6+x) = 66x instead of 66 + 11x = wrong coefficient! This creates an incorrect linear equation with the wrong solution. Always distribute each factor completely: 11(6+x) = 66 + 11x.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

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

FAQ

Everything you need to know about this question

Why can't I just multiply both sides by (x+5)?

You could, but cross-multiplication is more efficient when you have one fraction equal to another fraction. It eliminates both denominators in one step!

What if x+5 equals zero in my answer?

Great question! If your solution makes the denominator zero, that answer is invalid. Always check that x ≠ -5 in this problem, since that would make the fraction undefined.

How do I handle the decimal answer -6.57?

The exact answer is $\frac{-46}{7}$ . You can leave it as a fraction or convert to decimal. Both forms are correct, but fractions are often preferred for exact values.

Can I check my work without substituting back?

Substitution is the best verification method, but you can also check your algebra steps. Make sure your cross-multiplication and distribution are correct at each step.

What if I get a positive answer instead?

Double-check your signs! When you get $7x = -46$ , dividing by positive 7 gives a negative result. Sign errors are very common in multi-step problems.

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Solve the Rational Equation: Finding X in (6+x)/(x+5) = 4/11

Cross-Multiplication with Rational Equations

❤️ 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

Why can't I just multiply both sides by (x+5)?

What if x+5 equals zero in my answer?

How do I handle the decimal answer -6.57?

Can I check my work without substituting back?

What if I get a positive answer instead?

🌟 Unlock Your Math Potential

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