Question

Rewrite the equation below so that it does not have fractions. 2/3x-2=3/4 Do not use decimals in your answer. x= ?

Answer 1

To rewrite the equation \( \frac{2}{3}x - 2 = \frac{3}{4} \) without fractions, we can first find a common denominator for all the terms in the equation. The common denominator for 3 and 4 is 12.

We can multiply the entire equation by 12 to eliminate the fractions:

\[
12 \left(\frac{2}{3}x\right) - 12(2) = 12\left(\frac{3}{4}\right)
\]

Now, simplifying each term:

\[
12 \cdot \frac{2}{3}x = 8x \quad \text{(since } 12 \div 3 = 4 \text{ and } 4 \cdot 2 = 8\text{)}
\]
\[
12 \cdot (-2) = -24
\]
\[
12 \cdot \frac{3}{4} = 9 \quad \text{(since } 12 \div 4 = 3 \text{ and } 3 \cdot 3 = 9\text{)}
\]

Putting it all together, we have:

\[
8x - 24 = 9
\]

Next, we can solve for \( x \):

1. Add 24 to both sides:

\[
8x = 9 + 24
\]
\[
8x = 33
\]

2. Finally, divide by 8:

\[
x = \frac{33}{8}
\]

Thus, the final answer is:

\[
x = \frac{33}{8}
\]