Question

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 \(a(b - c)=ab - ac\), where \(a = 8\), \(b=x\), \(c = 3\). So \(8(x-3)=8x-8\times3=8x - 24\). So this expression is equivalent.

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

First, factor out \((x - 3)\): \(9(x - 3)-(x - 3)=(9 - 1)(x - 3)=8(x - 3)\). Then, using the distributive property as above, \(8(x - 3)=8x-24\). So this expression is equivalent.

Step3: Analyze \(8(x - 24)\)

Using the distributive property: \(8(x - 24)=8x-8\times24=8x - 192
eq8x - 24\). So this is not equivalent.

Step4: Analyze \((5 + 3)x-24\)

Simplify \(5 + 3 = 8\), so \((5 + 3)x-24=8x-24\). So this expression is equivalent.

Step5: Analyze \(16x\)

\(16x\) is a single - term expression with coefficient 16, while \(8x-24\) has two terms with coefficient 8 for \(x\) and constant term - 24. So \(16x
eq8x - 24\).

Answer:

The equivalent expressions are:

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