Find the solution to the inequality 18>3/2(4w−4)

Question

.(1 point)
Responses

w<108
w less than Start Fraction 10 over 8 End Fraction

w>108
w greater than Start Fraction 10 over 8 End Fraction

w<4
w less than 4

w>4

Answer 1

To solve the inequality \( 18 > \frac{3}{2}(4w - 4) \), we can follow these steps:

1. Distribute \( \frac{3}{2} \) on the right side: \[ 18 > \frac{3}{2}(4w) - \frac{3}{2}(4) \] \[ 18 > 6w - 6 \]

2. Add 6 to both sides: \[ 18 + 6 > 6w \] \[ 24 > 6w \]

3. Divide both sides by 6: \[ \frac{24}{6} > w \] \[ 4 > w \] or equivalently, \[ w < 4 \]

Thus, the solution to the inequality is \( w < 4 \).

The correct response is: w < 4