how many solutions exist for the given equation?\n$\frac{1}{2}(x + 12)=4x - 1$\nzero\none\ntwo\ninfinitely…

Answer:

B. one

Explanation:

Step1: Expand the left - hand side

$\frac{1}{2}(x + 12)=\frac{1}{2}x+6$ The equation becomes $\frac{1}{2}x + 6=4x-1$.

Step2: Move the $x$ terms to one side

Subtract $\frac{1}{2}x$ from both sides: $6 = 4x-\frac{1}{2}x-1$. Combine like - terms: $6=\frac{8x - x}{2}-1$, so $6=\frac{7x}{2}-1$.

Step3: Isolate the $x$ term

Add 1 to both sides: $6 + 1=\frac{7x}{2}$, so $7=\frac{7x}{2}$.

Step4: Solve for $x$

Multiply both sides by $\frac{2}{7}$: $x = 2$. Since we found a single value for $x$, there is one solution.