Solve the Fraction Equation: Find X in (x+2)/3 = 4/5

Q: When can I use cross-multiplication?

Cross-multiplication works when you have one fraction equals another fraction, like $ \frac{a}{b} = \frac{c}{d} $. If there are addition or subtraction between fractions, use LCD method instead.

Q: How do I know if I distributed correctly?

After writing $ 5(x+2) $, multiply 5 by each term inside: $ 5 \cdot x + 5 \cdot 2 = 5x + 10 $. Don't forget any terms!

Q: What if my final answer doesn't look like the choices?

Check if your fraction can be simplified or converted to a mixed number. Also verify by substituting back - if it works in the original equation, your answer is correct regardless of format.

Q: Can I solve this without cross-multiplication?

Yes! You can multiply both sides by 3 first: $ x + 2 = \frac{12}{5} $, then subtract 2. You'll get the same answer: $ x = \frac{2}{5} $.

Cross-Multiplication with Fractional Equations

Solve for X:

$\frac{x+2}{3}=\frac{4}{5}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's solve the problem.

00:11 Our goal is to find the value of X.

00:15 First, we multiply by both denominators. This helps remove any fractions.

00:25 Next, we open the parentheses and multiply each term carefully.

00:36 Now, let's rearrange the equation to have X on just one side.

00:50 Finally, we isolate X to find its value.

00:54 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$\frac{x+2}{3}=\frac{4}{5}$

Step-by-step solution

To solve the equation $\frac{x+2}{3}=\frac{4}{5}$ , we can follow the method of cross-multiplication:

Step 1: Cross-multiply to eliminate the fractions, giving us:

$(x + 2) \cdot 5 = 4 \cdot 3$

Step 2: Simplify both sides of the equation:

$5(x + 2) = 12$

Step 3: Distribute the 5 on the left side:

$5x + 10 = 12$

Step 4: Subtract 10 from both sides to isolate the term with $x$ :

$5x = 2$

Step 5: Divide both sides by 5 to solve for $x$ :

$x = \frac{2}{5}$

Therefore, the solution to the equation is $\frac{2}{5}$ .

Final Answer

$\frac{2}{5}$

Key Points to Remember

Essential concepts to master this topic

Cross-Multiplication Rule: When fraction equals fraction, multiply diagonally across
Technique: $(x+2) \cdot 5 = 4 \cdot 3$ gives $5x + 10 = 12$
Check: Substitute $x = \frac{2}{5}$ : $\frac{\frac{2}{5}+2}{3} = \frac{4}{5}$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute after cross-multiplication
Don't write $5(x+2) = 12$ and then solve $5x = 12$ = $x = \frac{12}{5}$ ! You missed distributing the 5, so you forgot the +10 term completely. Always distribute: $5x + 10 = 12$ , then $5x = 2$ .

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 when you have one fraction equals another fraction, like $\frac{a}{b} = \frac{c}{d}$ . If there are addition or subtraction between fractions, use LCD method instead.

Why do I get a different answer when I multiply both sides by 15?

Multiplying by 15 (the LCD of 3 and 5) also works! You'd get $5(x+2) = 12$ , which is the same result as cross-multiplication. Both methods are correct.

How do I know if I distributed correctly?

After writing $5(x+2)$ , multiply 5 by each term inside: $5 \cdot x + 5 \cdot 2 = 5x + 10$ . Don't forget any terms!

What if my final answer doesn't look like the choices?

Check if your fraction can be simplified or converted to a mixed number. Also verify by substituting back - if it works in the original equation, your answer is correct regardless of format.

Can I solve this without cross-multiplication?

Yes! You can multiply both sides by 3 first: $x + 2 = \frac{12}{5}$ , then subtract 2. You'll get the same answer: $x = \frac{2}{5}$ .

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