Solve the equation using the distributive property and properties of equality.

Question

One-half (x + 6) = 18

What is the value of x?
6
7 and one-half
14 and one-half
30

Answer 1

To solve the equation \(\frac{1}{2} (x + 6) = 18\), we will use the distributive property and properties of equality.

1. Apply the distributive property: Multiply \(\frac{1}{2}\) by both \(x\) and \(6\): \[ \frac{1}{2} x + \frac{1}{2} \cdot 6 = 18 \] This simplifies to: \[ \frac{1}{2} x + 3 = 18 \]

2. Isolate the term with \(x\): Subtract \(3\) from both sides: \[ \frac{1}{2} x = 18 - 3 \] This simplifies to: \[ \frac{1}{2} x = 15 \]

3. Eliminate the fraction: Multiply both sides by \(2\) to solve for \(x\): \[ x = 15 \cdot 2 \] This simplifies to: \[ x = 30 \]

Thus, the value of \(x\) is \(30\).