Question

Which of the following equations have the same solution? Solve all three equations separately and explain each step.

I. 2x + 4 = 3x – 11
II. 3x + 3 = 51
III. the quantity of 2x plus 1, divided by 3 equals the quantity of x plus 6, divided by 2

Answer 1

1. 2x + 4 = 3x - 11 -- subtract 3x from both sides
2x - 3x + 4 = -11 --- subtract 4 from each side
2x - 3x = -11 - 4 -- combine like terms
-x = - 15
x = 15

2. 3x + 3 = 51 -- subtract 3 from both sides
3x = 51 - 3
3x = 48 -- divide both sides by 3
x = 48/3
x = 16

3. (2x + 1) /3 = (x + 6)/2
cross multiply
3(x + 6) = 2(2x + 1) -- distribute
3x + 18 = 4x + 2 -- subtract 4x from both sides
3x - 4x + 18 = 2 -- subtract 18 from both sides
3x - 4x = 2 - 18 -- combine like terms
-x = -16
x = 16