Question

1. select each expression that is equivalent to 5(n + 4).

□ 5n + 4
□ 5n + 20
□ 15 + 5n + 5
□ 5(n + 3) + 5
□ 5n + 54

Explanation:

Step1: Expand \(5(n + 4)\)

Using the distributive property \(a(b + c)=ab+ac\), we have \(5(n + 4)=5\times n+5\times4 = 5n+20\).

Step2: Analyze \(5n + 4\)

Compare with \(5n + 20\), \(5n+4
eq5n + 20\), so it is not equivalent.

Step3: Analyze \(5n + 20\)

This is the expanded form of \(5(n + 4)\), so it is equivalent.

Step4: Analyze \(15 + 5n+5\)

Simplify \(15 + 5n+5=5n+(15 + 5)=5n + 20\), which is equivalent to \(5(n + 4)\).

Step5: Analyze \(5(n + 3)+5\)

Expand \(5(n + 3)+5=5n+15 + 5=5n+20\), which is equivalent to \(5(n + 4)\).

Step6: Analyze \(5n + 54\)

Compare with \(5n + 20\), \(5n+54
eq5n + 20\), so it is not equivalent.

Answer:

The equivalent expressions are:

• \(5n + 20\)
• \(15 + 5n + 5\)
• \(5(n + 3)+5\)