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= ? X 5

Answer 1

To eliminate fractions from the equation \( \frac{2}{3}x - 2 = \frac{3}{4} \), we can find a common multiple of the denominators 3 and 4. The least common multiple of 3 and 4 is 12.

Now, we will multiply the entire equation by 12 to eliminate the fractions:

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

Distributing 12 gives:

\[
12 \cdot \frac{2}{3}x - 12 \cdot 2 = 12 \cdot \frac{3}{4}
\]

Calculating each term:

\[
4 \cdot 2x - 24 = 9
\]

This simplifies to:

\[
8x - 24 = 9
\]

Next, we can add 24 to both sides:

\[
8x = 33
\]

Finally, divide by 8:

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

Thus, when multiplying \( x \) by 5:

\[
x \cdot 5 = \frac{33}{8} \cdot 5 = \frac{165}{8}
\]

So the final answer is:

\[
x \cdot 5 = \frac{165}{8}
\]