Question

Rewrite the equation 4x/3x−12 + 3 = 10 in two equations joined by “and.”(2 points)

Answer 1

To rewrite the equation \( \frac{4x}{3x - 12} + 3 = 10 \) in two equations joined by "and," we'll first isolate the fraction and then state the resulting equations.

1. Starting with the original equation:
\[
\frac{4x}{3x - 12} + 3 = 10
\]

2. Subtract 3 from both sides:
\[
\frac{4x}{3x - 12} = 7
\]

Now we can express this as two separate equations:
1. \( \frac{4x}{3x - 12} = 7 \)
2. \( 3x - 12 \neq 0 \) (to avoid division by zero, implying \( x \neq 4 \))

Thus, the rewritten form is:
\[
\frac{4x}{3x - 12} = 7 \quad \text{and} \quad x \neq 4
\]