Question

how many solutions exist for the given equation?
\\(\frac{1}{2}(x + 12) = 4x - 1\\)
\\(\circ\\) zero
\\(\circ\\) one
\\(\circ\\) two
\\(\circ\\) infinitely many

Explanation:

Step1: Simplify left side

Multiply out $\frac{1}{2}(x + 12)$: $\frac{1}{2}x + 6$

Step2: Set equation

Now equation is $\frac{1}{2}x + 6 = 4x - 1$

Step3: Solve for x

Subtract $\frac{1}{2}x$: $6 = \frac{7}{2}x - 1$
Add 1: $7 = \frac{7}{2}x$
Multiply by $\frac{2}{7}$: $x = 2$
One solution as x has unique value.

Answer:

one (the option with "one")