After distributing, focus on the constant (number) terms on the left side. Rewrite whole numbers as fractions with a common denominator so you can add or subtract them accurately.

Once you have an equation with fractions, multiply both sides by a common denominator (such as 4) to clear the fractions, then collect all $x$ terms on one side and constants on the other.

In Desmos, type y = (3/4)(x - 2) + 5 for the left-hand side and y = (1/2)(x + 6) for the right-hand side. You will see two lines on the graph.

Adjust the viewing window if needed so the point where the two lines cross is visible. Tap or click on the intersection point and note the x-coordinate; that x-value is the solution to the equation.

Start with the given equation:

Use the distributive property on both sides:

• Left side: $\frac{3}{4}(x - 2) = \frac{3}{4}x - \frac{3}{2}$
• Right side: $\frac{1}{2}(x + 6) = \frac{1}{2}x + 3$

So the equation becomes:

On the left side, combine the constant terms $-\frac{3}{2}$ and $5$.

Write $5$ as a fraction with denominator 2: $5 = \frac{10}{2}$.

Then:

So the equation is now:

To eliminate fractions, multiply every term on both sides by 4 (the least common multiple of 4 and 2):

This simplifies to:

Now solve $3x + 14 = 2x + 12$.

1. Subtract $2x$ from both sides to get all $x$ terms on one side:

2. Subtract 14 from both sides to isolate $x$:

So the value of $x$ that satisfies the equation is $-2$, which corresponds to choice A.