Question

solve the equation. simplify your answer if possible. 7(c + 2) + 4 = 54 - (c + 4)

Explanation:

Step1: Expand both sides

Expand the left - hand side: \(7(c + 2)+4=7c+14 + 4=7c+18\)
Expand the right - hand side: \(54-(c + 4)=54 - c-4=50 - c\)
So the equation becomes \(7c+18 = 50 - c\)

Step2: Add c to both sides

Add \(c\) to each side of the equation \(7c+18 = 50 - c\) to get \(7c + c+18=50 - c + c\)
Simplify both sides: \(8c+18 = 50\)

Step3: Subtract 18 from both sides

Subtract 18 from both sides of the equation \(8c+18 = 50\): \(8c+18-18=50 - 18\)
Simplify both sides: \(8c=32\)

Step4: Divide both sides by 8

Divide both sides of the equation \(8c = 32\) by 8: \(\frac{8c}{8}=\frac{32}{8}\)
Simplify both sides: \(c = 4\)

Answer:

\(c = 4\)