Question

1. select each expression that is equivalent to 8x - 24.

□ 8(x - 3)
□ 8(x - 24)
□ 9(x - 3) - (x - 3)
□ (5 + 3)x - 24
□ 16x

Explanation:

Step1: Analyze \(8(x - 3)\)

Using the distributive property \(a(b - c)=ab - ac\), here \(a = 8\), \(b=x\), \(c = 3\). So \(8(x-3)=8x-24\).

Step2: Analyze \(9(x - 3)-(x - 3)\)

Factor out \((x - 3)\): \((9 - 1)(x - 3)=8(x - 3)\), then distribute to get \(8x-24\).

Step3: Analyze \((5 + 3)x-24\)

Simplify \(5 + 3 = 8\), so \((5 + 3)x-24=8x-24\).

Step4: Analyze \(8(x - 24)\)

Distribute: \(8x-192
eq8x - 24\).

Step5: Analyze \(16x\)

\(16x\) is not equivalent to \(8x-24\).

Answer:

• \(8(x - 3)\)
• \(9(x - 3)-(x - 3)\)
• \((5 + 3)x-24\)