Which of the following equations have the same solution? Give reasons for your answers that do not depend on solving the equations.

a. x + 3 = 5x - 4

b. x - 3 = 5x + 4

c. 2x + 8 = 5x - 3

d. 10x + 6 = 2x - 8

e. 10x - 8 = 2x + 6

f. 0.3 + x/10 = 1/2x - 0.4

Equations b and d have the same solutions, because if you multiply both sides of b by 2 and invert the constants you'll have equation d:

b: x - 3 = 5x + 4

b*2: 2x - 6 = 10x + 8

Move - 6 and + 8 to the other side: 2x - 8 = 10x + 6 <- - this is equation d

Similarly, starting from equation a, you can obtain equation e by multiplying both sides by 2 and equation f by dividing both sides by 10.

Equation c has nothing in common with the others.