Solve for X in (5+3x)/x = 3/4: Rational Equation Solution

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

You can cross-multiply because you have one fraction equal to another fraction. When $ \frac{a}{b} = \frac{c}{d} $, then a×d = b×c. This eliminates both denominators at once!

Q: What if x is in the denominator like this problem?

Be careful! Since x is in the denominator, x cannot equal zero (division by zero is undefined). Always check that your final answer doesn't make any denominator zero.

Q: Do I need to worry about x = 0 in this problem?

Yes! Since our answer is $ x = -\frac{20}{9} $, which is not zero, we're safe. But always remember to check that your solution doesn't make the original equation undefined.

Q: How do I handle the fraction in my final answer?

The fraction $ -\frac{20}{9} $ is already in lowest terms since 20 and 9 share no common factors. Keep it as a fraction - don't convert to decimal unless specifically asked!

Q: Can I check my answer without substituting back?

Always substitute back! It's the most reliable way to catch errors. When you substitute $ x = -\frac{20}{9} $, both sides should equal $ \frac{3}{4} $.

Cross-Multiplication with Rational Expressions

Solve for X:

$\frac{5+3x}{x}=\frac{3}{4}$

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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 denominators to eliminate fractions

00:22 Simplify as much as possible

00:31 Carefully open parentheses properly, multiply by each factor

00:48 Arrange the equation so that one side has only the unknown X

01:06 Collect like terms

01:14 Isolate X

01:21 Simplify as much as possible

01:24 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:

$\frac{5+3x}{x}=\frac{3}{4}$

Step-by-step solution

Let's solve the equation $\frac{5+3x}{x} = \frac{3}{4}$ .

Step 1: Begin by applying cross-multiplication to eliminate the fractions. This gives us:

$(5 + 3x) \cdot 4 = 3 \cdot x$
Simplifying, we get:
$20 + 12x = 3x$

Step 2: Rearrange the equation to bring all terms involving $x$ to one side:

$20 + 12x - 3x = 0$
Simplifying, we find:
$20 + 9x = 0$

Step 3: Isolate $x$ by solving the equation:

$9x = -20$
Divide both sides by 9 to solve for $x$ :
$x = -\frac{20}{9}$

Therefore, the solution to the equation $\frac{5+3x}{x} = \frac{3}{4}$ is $x = -\frac{20}{9}$ .

Final Answer

$-\frac{20}{9}$

Key Points to Remember

Essential concepts to master this topic

Rule: Cross-multiply when equation has one fraction on each side
Technique: (5+3x)×4 = 3×x gives 20+12x = 3x
Check: Substitute $x = -\frac{20}{9}$ back into original equation ✓

Common Mistakes

Avoid these frequent errors

Distributing incorrectly after cross-multiplication
Don't write 4(5+3x) as 4×5 + 3x = 20+3x! This misses multiplying 4 by the 3x term, giving wrong coefficients. Always distribute to every term: 4(5+3x) = 4×5 + 4×3x = 20+12x.

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 I cross-multiply in this equation?

You can cross-multiply because you have one fraction equal to another fraction. When $\frac{a}{b} = \frac{c}{d}$ , then a×d = b×c. This eliminates both denominators at once!

What if x is in the denominator like this problem?

Be careful! Since x is in the denominator, x cannot equal zero (division by zero is undefined). Always check that your final answer doesn't make any denominator zero.

Do I need to worry about x = 0 in this problem?

Yes! Since our answer is $x = -\frac{20}{9}$ , which is not zero, we're safe. But always remember to check that your solution doesn't make the original equation undefined.

How do I handle the fraction in my final answer?

The fraction $-\frac{20}{9}$ is already in lowest terms since 20 and 9 share no common factors. Keep it as a fraction - don't convert to decimal unless specifically asked!

Can I check my answer without substituting back?

Always substitute back! It's the most reliable way to catch errors. When you substitute $x = -\frac{20}{9}$ , both sides should equal $\frac{3}{4}$ .

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Solve for X in (5+3x)/x = 3/4: Rational Equation Solution

Cross-Multiplication with Rational Expressions

❤️ 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 I cross-multiply in this equation?

What if x is in the denominator like this problem?

Do I need to worry about x = 0 in this problem?

How do I handle the fraction in my final answer?

Can I check my answer without substituting back?

🌟 Unlock Your Math Potential

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