Question

c. 2c - 3 = 2(6 - c) + 7c
c = \square

Explanation:

Step1: Expand the right side

First, we expand the right - hand side of the equation \(2(6 - c)+7c\) using the distributive property \(a(b + c)=ab+ac\). Here, \(a = 2\), \(b = 6\) and \(c=-c\), so \(2(6 - c)=2\times6-2\times c = 12-2c\). Then 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 all the \(c\) terms on one side. \((2c-3)-2c=(12 + 5c)-2c\), which simplifies to \(-3=12 + 3c\).

Step4: Solve for c

Subtract 12 from both sides: \(-3-12=12 + 3c-12\), so \(-15 = 3c\). Then divide both sides by 3: \(\frac{-15}{3}=\frac{3c}{3}\), which gives \(c=- 5\).

Answer:

\(-5\)