Question

which expression is equivalent to -3x + 5.1? a -3(x + 1.7) b -3(x - 1.7) c 3(x + 1.7) d 3(x - 1.7)

Explanation:

Step1: Recall distributive property

The distributive property is \(a(b + c)=ab+ac\) and \(a(b - c)=ab - ac\). We need to expand each option and see which one matches \(-3x + 5.1\).

Step2: Expand Option A

Expand \(-3(x + 1.7)\) using distributive property:
\(-3\times x+(-3)\times1.7=-3x - 5.1\). This does not match.

Step3: Expand Option B

Expand \(-3(x - 1.7)\) using distributive property:
\(-3\times x-(-3)\times1.7=-3x + 5.1\). This matches the given expression.

Step4: Verify other options (optional)

Expand Option C: \(3(x + 1.7)=3x+5.1\), does not match.
Expand Option D: \(3(x - 1.7)=3x - 5.1\), does not match.

Answer:

B. \(-3(x - 1.7)\)