Question

VARIABLE EQUATIONS & INEQUALITIES UNIT TEST:
REWRITE THE EQUATION \frac{4x}{3x-12}+3=10 IN TWO EQUATIONS JOINED BY "AND."

Answer 1

To rewrite the equation \(\frac{4x}{3x-12} + 3 = 10\) in two equations joined by "AND," we need to isolate the fraction and then set up a corresponding equation that reflects the relationship.

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

2. Subtract 3 from both sides to isolate the fraction:
\[
\frac{4x}{3x-12} = 10 - 3
\]
\[
\frac{4x}{3x-12} = 7
\]

Now, we have two statements that can be expressed as separate equations:

- The fraction equation:
\[
\frac{4x}{3x-12} = 7
\]

- The condition that we simplified (the right side of the original equation):
\[
3x - 12 \neq 0
\]
(because the denominator cannot equal zero)

Now, we can combine these into a statement with "AND":

\[
\frac{4x}{3x-12} = 7 \quad \text{AND} \quad 3x - 12 \neq 0
\]

So the final answer is:

\[
\frac{4x}{3x-12} = 7 \quad \text{AND} \quad 3x \neq 12
\]