Question

Rewrite the equation for x over 3x - 12 + 3 = 10 and two equations joined by and

Answer 1

To rewrite the equation \( \frac{x}{3x - 12} + 3 = 10 \), we first isolate the fraction:

1. Subtract 3 from both sides:
\[
\frac{x}{3x - 12} = 10 - 3
\]
\[
\frac{x}{3x - 12} = 7
\]

2. Multiply both sides by \( 3x - 12 \) (assuming \( 3x - 12 \neq 0 \)) to eliminate the fraction:
\[
x = 7(3x - 12)
\]

3. Expand the right side:
\[
x = 21x - 84
\]

4. Rearrange it to get all terms involving \( x \) on one side:
\[
x - 21x = -84
\]
\[
-20x = -84
\]

5. Divide by -20:
\[
x = \frac{84}{20}
\]
\[
x = \frac{21}{5}
\]

Thus, the equation can be rewritten and solved as follows:
\[
\frac{x}{3x - 12} + 3 = 10 \iff x = \frac{21}{5}
\]

If you want to express this in the context of two equations joined by "and," you might write:

1. \( \frac{x}{3x - 12} + 3 = 10 \)
2. \( x = \frac{21}{5} \)

So, it can be expressed as:
\[
\frac{x}{3x - 12} + 3 = 10 \quad \text{and} \quad x = \frac{21}{5}
\]