Question

use the zero product property to solve (2x - 3)(x + 4) = 0. (2 points)
x = 1.5

x =

4 0 -3 -4

Explanation:

Step1: Apply Zero Product Property

The Zero Product Property states that if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \). For the equation \( (2x - 3)(x + 4)=0 \), we set each factor equal to zero:

• \( 2x - 3 = 0 \)
• \( x + 4 = 0 \)

Step2: Solve \( 2x - 3 = 0 \)

Add 3 to both sides: \( 2x = 3 \). Then divide by 2: \( x=\frac{3}{2}=1.5 \).

Step3: Solve \( x + 4 = 0 \)

Subtract 4 from both sides: \( x=-4 \).

Answer:

The solutions are \( x = 1.5 \) and \( x=-4 \).