Solve the Fraction Equation: Finding X in (x+4)/3 = 7/8

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} $. This gives you ad = bc.

Q: How do I convert -11/8 to a mixed number?

Divide 11 by 8: 11 ÷ 8 = 1 remainder 3. So $ -\frac{11}{8} = -1\frac{3}{8} $. The negative sign goes with the whole mixed number.

Q: Why did we get a negative answer?

We got x = $ -1\frac{3}{8} $ because when we solved 8x = 21 - 32, we had 8x = -11. The subtraction 21 - 32 gives a negative result.

Q: Can I check my answer using decimals?

Yes! Convert $ -1\frac{3}{8} = -1.375 $. Then check: $ \frac{-1.375+4}{3} = \frac{2.625}{3} = 0.875 $ and $ \frac{7}{8} = 0.875 $ ✓

Cross-Multiplication with Mixed Number Solutions

Solve for X:

$\frac{x+4}{3}=\frac{7}{8}$

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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

00:07 Multiply by both denominators to eliminate fractions

00:17 Open parentheses properly, multiply by each term

00:29 Arrange the equation so that one side has only the unknown X

00:39 Isolate the unknown X

00:48 Reduce what's possible

00:53 Break down (-11) to (-8) minus 3

00:59 Break down the fraction into a whole number and remainder

01:06 Convert the whole fraction to a whole number

01:13 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:

$\frac{x+4}{3}=\frac{7}{8}$

Step-by-step solution

First, we cross multiply:

$8\times(x+4)=3\times7$

We multiply the right section and expand the parenthesis, multiplying each of the terms by 8:

$8x+32=21$

We rearrange the equation remembering change the plus and minus signs accordingly:

$8x=21-32$
Solve the subtraction exercise on the right side and divide by 8:

$8x=-11$

$\frac{8x}{8}=-\frac{11}{8}$

Convert the simple fraction into a mixed fraction:

$x=-1\frac{3}{8}$

Final Answer

$-1\frac{3}{8}$

Key Points to Remember

Essential concepts to master this topic

Rule: Cross-multiply when one fraction equals another fraction
Technique: 8(x+4) = 3×7 becomes 8x + 32 = 21
Check: Substitute $-1\frac{3}{8}$ : $\frac{-1\frac{3}{8}+4}{3} = \frac{7}{8}$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute when expanding parentheses
Don't write 8(x+4) = 8x + 4 = wrong answer of x = 17/8! This ignores the 8 that multiplies the 4 inside parentheses. Always distribute: 8(x+4) = 8x + 32.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

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 $\frac{a}{b} = \frac{c}{d}$ . This gives you ad = bc.

How do I convert -11/8 to a mixed number?

Divide 11 by 8: 11 ÷ 8 = 1 remainder 3. So $-\frac{11}{8} = -1\frac{3}{8}$ . The negative sign goes with the whole mixed number.

Why did we get a negative answer?

We got x = $-1\frac{3}{8}$ because when we solved 8x = 21 - 32, we had 8x = -11. The subtraction 21 - 32 gives a negative result.

Can I check my answer using decimals?

Yes! Convert $-1\frac{3}{8} = -1.375$ . Then check: $\frac{-1.375+4}{3} = \frac{2.625}{3} = 0.875$ and $\frac{7}{8} = 0.875$ ✓

What if I made an arithmetic error?

Double-check each step: 8×7 = 56? No, 8×7 = 56 is wrong! It should be 3×7 = 21. Also verify 21 - 32 = -11, not +11.

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