Solve for X in the Equation x/(3+2x) = 1/5: Rational Expression Problem

Q: Why do I need to check my answer?

Rational equations can sometimes produce extraneous solutions that make denominators zero. Always substitute back to ensure your answer doesn't create division by zero!

Q: What if the denominator contains my variable?

That's exactly what makes this a rational equation! Just remember to keep the entire denominator together when cross-multiplying, like treating $ (3+2x) $ as one unit.

Q: Can I solve this without cross-multiplying?

Yes! You could multiply both sides by $ 5(3+2x) $ to clear fractions. But cross-multiplication is usually faster and cleaner when you have this fraction-equals-fraction setup.

Q: How do I know when to use parentheses?

Always put parentheses around multi-term denominatorsIn our problem: $ 5x = 1(3+2x) $ not $ 5x = 1 \cdot 3 + 2x $This ensures you distribute correctly!

Rational Equations with Cross-Multiplication Method

Solve for X:

$\frac{x}{3+2x}=\frac{1}{5}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:04 Multiply by denominators to eliminate fractions

00:26 Simplify as much as possible

00:40 Arrange the equation so that X is isolated on one side

00:58 Isolate X

01:07 Simplify as much as possible

01:12 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:

$\frac{x}{3+2x}=\frac{1}{5}$

Step-by-step solution

To solve the equation $\frac{x}{3+2x} = \frac{1}{5}$ , we will perform the following steps:

Step 1: Cross-multiply to eliminate the fractions.
Step 2: Simplify the resulting equation and solve for $x$ .

Now, let's work through these steps:

Step 1: Cross-multiply the equation $\frac{x}{3+2x} = \frac{1}{5}$ to obtain:

$5x = 1(3 + 2x)$

Step 2: Distribute the 1 on the right-hand side:

$5x = 3 + 2x$

Subtract $2x$ from both sides to begin isolating $x$ :

$5x - 2x = 3$

$3x = 3$

Divide both sides by 3 to solve for $x$ :

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

$x = 1$

Therefore, the solution to the problem is $\boxed{1}$ .

The correct answer, matching the given choices, is therefore choice $2$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Cross-Multiplication Rule: When $\frac{a}{b} = \frac{c}{d}$ , then $ad = bc$
Distribution Technique: From $5x = 1(3 + 2x)$ distribute to get $5x = 3 + 2x$
Verification Check: Substitute $x = 1$ back: $\frac{1}{3+2(1)} = \frac{1}{5}$ ✓

Common Mistakes

Avoid these frequent errors

Incorrectly cross-multiplying complex expressions
Don't cross-multiply $\frac{x}{3+2x} = \frac{1}{5}$ as $x \cdot 5 = 1 \cdot 3+2x$ = missing parentheses around the denominator! This gives $5x = 3+2x$ instead of $5x = 1(3+2x)$ . Always treat the entire denominator as one unit when cross-multiplying.

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

What exactly is cross-multiplication?

Cross-multiplication is a shortcut for solving equations with one fraction on each side. When you have $\frac{a}{b} = \frac{c}{d}$ , you multiply diagonally: a times d equals b times c.

Why do I need to check my answer?

Rational equations can sometimes produce extraneous solutions that make denominators zero. Always substitute back to ensure your answer doesn't create division by zero!

What if the denominator contains my variable?

That's exactly what makes this a rational equation! Just remember to keep the entire denominator together when cross-multiplying, like treating $(3+2x)$ as one unit.

Can I solve this without cross-multiplying?

Yes! You could multiply both sides by $5(3+2x)$ to clear fractions. But cross-multiplication is usually faster and cleaner when you have this fraction-equals-fraction setup.

How do I know when to use parentheses?

Always put parentheses around multi-term denominators
In our problem: $5x = 1(3+2x)$ not $5x = 1 \cdot 3 + 2x$
This ensures you distribute correctly!

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Solve for X in the Equation x/(3+2x) = 1/5: Rational Expression Problem

Rational Equations with Cross-Multiplication Method

❤️ 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

What exactly is cross-multiplication?

Why do I need to check my answer?

What if the denominator contains my variable?

Can I solve this without cross-multiplying?

How do I know when to use parentheses?

🌟 Unlock Your Math Potential

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