Question

c 2c - 3 = 2(6 - c) + 7c

Explanation:

Step1: Expand the right side

First, we expand the right - hand side of the equation \(2c - 3=2(6 - c)+7c\). Using the distributive property \(a(b - c)=ab - ac\), we have \(2(6 - c)=12-2c\). So the equation becomes \(2c - 3 = 12-2c + 7c\).

Step2: Combine like terms on the right side

Combine the like terms \(-2c\) and \(7c\) on the right - hand side. \(-2c+7c = 5c\), so the equation is now \(2c - 3=12 + 5c\).

Step3: Move the variable terms to one side

Subtract \(2c\) from both sides of the equation to get \(-3=12 + 5c-2c\), which simplifies to \(-3 = 12+3c\).

Step4: Move the constant terms to the other side

Subtract 12 from both sides: \(-3-12=3c\), so \(-15 = 3c\).

Step5: Solve for c

Divide both sides by 3: \(c=\frac{-15}{3}=- 5\).

Answer:

\(c = - 5\)