Question

what value of b is a solution to this equation?
32 = -b + 6(12 + b)

b = -8

b = -6

Explanation:

Step1: Expand the right side

First, we expand \(6(12 + b)\) using the distributive property \(a(b + c)=ab+ac\). So \(6(12 + b)=6\times12+6\times b = 72+6b\). The equation becomes \(32=-b + 72+6b\).

Step2: Combine like terms

Combine the \(b\) terms on the right side: \(-b+6b = 5b\). So the equation is now \(32 = 5b+72\).

Step3: Isolate the variable term

Subtract 72 from both sides to get \(32 - 72=5b\). Calculating the left side: \(32-72=-40\), so \(-40 = 5b\).

Step4: Solve for b

Divide both sides by 5: \(b=\frac{-40}{5}=-8\). We can also check by plugging \(b = - 8\) and \(b=-6\) into the original equation. For \(b=-8\): Right side \(-(-8)+6(12+(-8))=8 + 6\times4=8 + 24 = 32\), which equals the left side. For \(b = - 6\): Right side \(-(-6)+6(12+(-6))=6+6\times6=6 + 36=42
eq32\). So \(b=-8\) is the solution.

Answer:

\(b=-8\) (the option \(b = - 8\))