Solve for X: Finding the Value in (9-x)/5 = x/4

Q: Why can't I just cross-multiply like a proportion?

You can cross-multiply! $ \frac{9-x}{5} = \frac{x}{4} $ gives you 4(9-x) = 5x. Just remember to distribute the 4 to get 36 - 4x = 5x.

Q: What's the difference between LCD method and cross-multiplying?

Both work perfectly! Cross-multiplying is faster for simple proportions, while LCD method works for any equation with fractions. Choose whichever feels easier to you.

Q: How do I handle the (9-x) in the numerator?

Treat (9-x) as a single unit when cross-multiplying. So 4(9-x) means you multiply 4 by everything inside: 4×9 - 4×x = 36 - 4x.

Q: Why do I get x = 4 and not x = 3?

Let's check both! If x = 3: $ \frac{9-3}{5} = \frac{6}{5} $ and $ \frac{3}{4} $ - these aren't equal. If x = 4: $ \frac{9-4}{5} = 1 $ and $ \frac{4}{4} = 1 $ ✓

Linear Equations with Cross-Multiplying Fractions

Solve for X:

$\frac{9-x}{5}=\frac{x}{4}$

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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

00:14 Simplify as much as possible

00:25 Carefully open parentheses correctly, multiply by each factor

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

00:51 Collect like terms

01:00 Isolate X

01:07 Simplify as much as possible

01:10 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:

$\frac{9-x}{5}=\frac{x}{4}$

Step-by-step solution

To solve the equation $\frac{9-x}{5} = \frac{x}{4}$ , follow these steps:

Multiply both sides of the equation by 20 to eliminate the fractions:

$20 \left(\frac{9-x}{5}\right) = 20 \left(\frac{x}{4}\right)$

Simplify both sides to eliminate the fractions:

The left side: $20 \times \frac{9-x}{5}$ simplifies to $4(9-x)$
The right side: $20 \times \frac{x}{4}$ simplifies to $5x$

Expand and simplify the equation:

$4(9-x) = 5x$

$36 - 4x = 5x$

Add $4x$ to both sides to collect all terms involving $x$ on the right:

$36 = 5x + 4x$

Simplify the equation:

$36 = 9x$

Divide both sides by 9 to solve for $x$ :

$x = \frac{36}{9}$

$x = 4$

Therefore, the solution to the equation is $x = 4$ .

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both sides by LCD to eliminate fractions completely
Technique: LCD of 5 and 4 is 20, so multiply: 20(9-x)/5 = 20x/4
Check: Substitute x = 4: (9-4)/5 = 1 and 4/4 = 1 ✓

Common Mistakes

Avoid these frequent errors

Cross-multiplying incorrectly with compound fractions
Don't try to cross-multiply (9-x)/5 = x/4 by writing (9-x)×4 = 5×x directly = wrong setup! This ignores proper distribution. Always multiply both sides by the LCD first, then distribute carefully.

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 cross-multiply like a proportion?

You can cross-multiply! $\frac{9-x}{5} = \frac{x}{4}$ gives you 4(9-x) = 5x. Just remember to distribute the 4 to get 36 - 4x = 5x.

What's the difference between LCD method and cross-multiplying?

Both work perfectly! Cross-multiplying is faster for simple proportions, while LCD method works for any equation with fractions. Choose whichever feels easier to you.

How do I handle the (9-x) in the numerator?

Treat (9-x) as a single unit when cross-multiplying. So 4(9-x) means you multiply 4 by everything inside: 4×9 - 4×x = 36 - 4x.

Why do I get x = 4 and not x = 3?

Let's check both! If x = 3: $\frac{9-3}{5} = \frac{6}{5}$ and $\frac{3}{4}$ - these aren't equal. If x = 4: $\frac{9-4}{5} = 1$ and $\frac{4}{4} = 1$ ✓

What if I make an algebra mistake after clearing fractions?

That's why checking is so important! Even if you clear fractions correctly, small algebra errors happen. Always substitute your final answer back into the original equation.

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Solve for X: Finding the Value in (9-x)/5 = x/4

Linear Equations with Cross-Multiplying Fractions

❤️ 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 cross-multiply like a proportion?

What's the difference between LCD method and cross-multiplying?

How do I handle the (9-x) in the numerator?

Why do I get x = 4 and not x = 3?

What if I make an algebra mistake after clearing fractions?

🌟 Unlock Your Math Potential

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