Question

fill in the missing column for each equation.

equation	common denominator of all terms	equation with denominators eliminated
b) $\frac{1}{2}-\frac{x}{3}=\frac{1}{3}$	6
c) $\frac{2}{3}=5 + x$	3

Explanation:

Step1: Multiply each term by common - denominator for a)

Multiply $\frac{3x}{4}+\frac{2}{3}=2$ by 12. We get $12\times\frac{3x}{4}+12\times\frac{2}{3}=12\times2$.
Simplify: $9x + 8=24$.

Step2: Multiply each term by common - denominator for b)

Multiply $\frac{1}{2}-\frac{x}{3}=\frac{1}{3}$ by 6. We get $6\times\frac{1}{2}-6\times\frac{x}{3}=6\times\frac{1}{3}$.
Simplify: $3 - 2x=2$.

Step3: Multiply each term by common - denominator for c)

Multiply $\frac{2}{3}=5 + x$ by 3. We get $3\times\frac{2}{3}=3\times(5 + x)$.
Simplify: $2 = 15+3x$.

Answer:

a) $9x + 8=24$
b) $3 - 2x=2$
c) $2 = 15+3x$