Question

1. $-\frac{1}{2}(12v - 20) + 4 = -12 - 8v$

Explanation:

Step1: Distribute the -1/2

Multiply \(-\frac{1}{2}\) with each term inside the parentheses: \(-\frac{1}{2} \times 12v = -6v\) and \(-\frac{1}{2} \times (-20) = 10\). So the left side becomes \(-6v + 10 + 4\).

Step2: Combine like terms on left

Add \(10\) and \(4\): \(-6v + 14 = -12 - 8v\).

Step3: Add 8v to both sides

To get all \(v\) terms on one side: \(-6v + 8v + 14 = -12 - 8v + 8v\), which simplifies to \(2v + 14 = -12\).

Step4: Subtract 14 from both sides

\(2v + 14 - 14 = -12 - 14\), so \(2v = -26\).

Step5: Divide by 2

Divide both sides by \(2\): \(v = \frac{-26}{2} = -13\).

Answer:

\(v = -13\)