Equations with brackets: Question 5 - Further consideration

Solve the following equation 3(4 – 6e) = 4(8 + 3e)

Solution

Given the equation 3(4 – 6e) = 4(8 + 3e)

The first step here is to remove brackets (ie open the brackets). We do this as follows

3(4 – 6e) = 4(8 + 3e)

3*4 – 3*6e = 4*8 + 4*3e

This gives

12 – 18e = 32 + 12e

The like terms have been painted for easy identification

Thus, next is to bring like terms together as follows

12 – 32 = 12e + 18e, which gives

-20 = 30e

Coefficient of e is 30. We now divide both sides by 30 to get the value of e as follows

^-20/₃₀ = ^30e/₃₀ and this becomes

^-2/₃ = e

e = ^-2/₃

Check for correctness

The given equation is 3(4 – 6e) = 4(8 + 3e)

LHS =   3(4 – 6e)

     =   3(4 – 6*(^-2/₃))

=   3(4 + 4)

=   3 * 8

=   24

RHS =   4(8 + 3e)

     =   4(8 + 3*(^-2/₃))

=   4(8 - 2)

=   4*6

     =   24 (Same as LHS)