Solving Linear Equations - Example3

Solve the following equation 6r + 2 = 3 + 3r + 1

Solution

Given the equation 6r + 2 = 3 + 3r + 1

The like terms in the equation 6r and 3r as well as 2, 3 and 1

Thus, we say bring like terms together as follows

6r + 2 = 3 + 3r + 1 (original equation)

6r – 3r = 3 + 1 – 2 (bringing like terms together)

You noticed in the above that +3r in the right hand side (RHS) crosses to the left hand side (LHS) to become -3r

Also, +2 in the left hand side (LHS) crosses the equality sign to the right hand side (RHS) to become -2

6r – 3r = 3 + 1 – 2

3r = 2

The coefficient of r is 3. To get r, we now divide both sides by 3 (coefficient of r) as follows

^3r/₃ = ²/₃

r = ²/₃

Check for correctness

The given equation is 6r + 2 = 3 + 3r + 1

LHS =   6r + 2

   =   6*²/₃) + 2

    =   4 + 2

    =   6

RHS =   3 + 3r + 1

    =   3 + 3*²/₃ + 1

    =   3 + 2 + 1

    =   6 (Same as LHS)