Question

which of the following is a solution to (2x - 9)(x + 8) = 0?
a: \\(\frac{9}{2}\\)
b: 8
c: 9
d: none of these
e: -2

Explanation:

Step1: Apply Zero-Product Property

If \((a)(b) = 0\), then either \(a = 0\) or \(b = 0\). For \((2x - 9)(x + 8)=0\), we set each factor equal to zero:

• Case 1: \(2x - 9 = 0\)
• Case 2: \(x + 8 = 0\)

Step2: Solve for \(x\) in Case 1

Solve \(2x - 9 = 0\):
Add 9 to both sides: \(2x = 9\)
Divide by 2: \(x=\frac{9}{2}\)

Step3: Solve for \(x\) in Case 2

Solve \(x + 8 = 0\):
Subtract 8 from both sides: \(x=-8\)

Among the options, \(\frac{9}{2}\) (Option A) is a solution.

Answer:

A. \(\frac{9}{2}\)