Solve the Fraction Equation: Discover X in (x - 4)/18 = 7/9

Q: When can I use cross-multiplication?

Cross-multiplication works only when you have one fraction equal to another fraction, like $ \frac{a}{b} = \frac{c}{d} $. If there are multiple terms or fractions, use the LCD method instead.

Q: Why do I get the wrong answer when I don't distribute?

After cross-multiplying $ 9(x-4) = 126 $, you must distribute the 9 to get $ 9x - 36 = 126 $. Skipping this step treats (x-4) as one unit, which is mathematically incorrect!

Q: How do I check if 18 is really the right answer?

Substitute x = 18 into the original equation: $ \frac{18-4}{18} = \frac{14}{18} = \frac{7}{9} $. Since both sides equal $ \frac{7}{9} $, our answer is correct!

Fraction Equations with Cross-Multiplication Method

Solve for X:

$\frac{x-4}{18}=\frac{7}{9}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to isolate the unknown X

00:06 We'll multiply by the reciprocal fraction to eliminate the fraction

00:18 We'll simplify what we can

00:27 We'll factor 18 into 9 and 2

00:33 We'll simplify what we can

00:38 We'll isolate the unknown X

00:47 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:

$\frac{x-4}{18}=\frac{7}{9}$

Step-by-step solution

To solve the equation $\frac{x-4}{18} = \frac{7}{9}$ , we'll follow these steps:

Step 1: Apply the principle of cross-multiplication to eliminate fractions.
Step 2: Solve for the linear expression in terms of $x$ .
Step 3: Isolate $x$ and solve the equation completely.

Now, let's work through each step:
Step 1: Cross-multiply to eliminate the fractions. The equation becomes:

$(x-4) \cdot 9 = 18 \cdot 7 \\ 9(x-4) = 126$

Step 2: Distribute the 9 on the left-hand side:

$9x - 36 = 126$

Step 3: Add 36 to both sides to isolate the term with $x$ :

$9x = 126 + 36 9x = 162$

Step 4: Divide both sides by 9 to solve for $x$ :

$x = \frac{162}{9} \\ x = 18$

Therefore, the solution to the equation is $x = 18$ .

Final Answer

$18$

Key Points to Remember

Essential concepts to master this topic

Cross-Multiplication Rule: When equation has one fraction equals another
Technique: $\frac{x-4}{18} = \frac{7}{9}$ becomes $9(x-4) = 18 \cdot 7$
Verification: Substitute x = 18: $\frac{18-4}{18} = \frac{14}{18} = \frac{7}{9}$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute after cross-multiplying
Don't write 9(x-4) = 126 and jump to 9x = 126! This skips the distribution step and gives x = 14 instead of 18. Always distribute first: 9x - 36 = 126, then solve step by step.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

When can I use cross-multiplication?

Cross-multiplication works only when you have one fraction equal to another fraction, like $\frac{a}{b} = \frac{c}{d}$ . If there are multiple terms or fractions, use the LCD method instead.

Why do I get the wrong answer when I don't distribute?

After cross-multiplying $9(x-4) = 126$ , you must distribute the 9 to get $9x - 36 = 126$ . Skipping this step treats (x-4) as one unit, which is mathematically incorrect!

How do I check if 18 is really the right answer?

Substitute x = 18 into the original equation: $\frac{18-4}{18} = \frac{14}{18} = \frac{7}{9}$ . Since both sides equal $\frac{7}{9}$ , our answer is correct!

What if the fractions don't simplify nicely?

That's okay! Cross-multiplication works with any fractions. Just be extra careful with your arithmetic when multiplying and make sure to simplify your final answer if possible.

Can I solve this equation differently?

Yes! You could multiply both sides by 18, then by 9 to clear fractions. But cross-multiplication is usually faster and cleaner when you have one fraction equals another.

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