Question

1. fill in the missing column for each equation.

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

Explanation:

Step1: Find common denominator for a)

The denominators are 4 and 3. The least - common multiple of 4 and 3 is 12.

Step2: Eliminate denominators for a)

Multiply each term in $\frac{3x}{4}+\frac{2}{3}=2$ by 12: $12\times\frac{3x}{4}+12\times\frac{2}{3}=12\times2$, which simplifies to $9x + 8=24$.

Step3: Find common denominator for b)

The denominators are 2 and 3. The least - common multiple of 2 and 3 is 6.

Step4: Eliminate denominators for b)

Multiply each term in $\frac{1}{2}-\frac{x}{3}=\frac{1}{3}$ by 6: $6\times\frac{1}{2}-6\times\frac{x}{3}=6\times\frac{1}{3}$, which simplifies to $3 - 2x=2$.

Step5: Find common denominator for c)

The denominator is 3.

Step6: Eliminate denominators for c)

Multiply each term in $\frac{2}{3}=5 + x$ by 3: $3\times\frac{2}{3}=3\times(5 + x)$, which simplifies to $2 = 15+3x$.

Answer:

Equation	Common Denominator of All Terms	Equation with Denominators Eliminated
$\frac{1}{2}-\frac{x}{3}=\frac{1}{3}$	6	$3 - 2x=2$
$\frac{2}{3}=5 + x$	3	$2 = 15+3x$