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: Analyze Option A

Expand \(-3(x + 1.7)\) using the distributive property \(a(b + c)=ab+ac\). Here, \(a=-3\), \(b = x\), \(c = 1.7\). So \(-3(x + 1.7)=-3x-5.1\), which is not equivalent to \(-3x + 5.1\).

Step2: Analyze Option B

Expand \(-3(x - 1.7)\) using the distributive property \(a(b - c)=ab - ac\). Here, \(a=-3\), \(b = x\), \(c = 1.7\). So \(-3(x - 1.7)=-3x+5.1\), which is equivalent to the given expression \(-3x + 5.1\).

Step3: Analyze Option C

Expand \(3(x + 1.7)\) using the distributive property \(a(b + c)=ab+ac\). Here, \(a = 3\), \(b=x\), \(c = 1.7\). So \(3(x + 1.7)=3x+5.1\), which is not equivalent to \(-3x + 5.1\).

Step4: Analyze Option D

Expand \(3(x - 1.7)\) using the distributive property \(a(b - c)=ab - ac\). Here, \(a = 3\), \(b=x\), \(c = 1.7\). So \(3(x - 1.7)=3x-5.1\), which is not equivalent to \(-3x + 5.1\).

Answer:

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