Solve the equation |3x +4a| = 5a where a is a positive constant.

This is a modulus question, asking us to solve for x. As there are two variables in this equation, it is impossible for us to solve for an actual number, so we are asked to answer in terms of a. The easiest way to solve this form of modulus question is to first answer as if 5a is positive - thus 5a - then as if it is negative - thus -5a. This is because although a modulus equation is always positive, when we remove the modulus its contents may be either positive or negative, following the understanding that |3x +4a| is the same as |3x + 4a| and |-(3x +4a). Thus, in the first instance we should solve:3x +4a = 5a3x = ax = a/3
Then to ensure we get all the answers:3x +4a = -5a3x = -9ax = -3a
We can draw a diagram too to help check that our answers seem reasonable. Thus in this case x = -3a and a/3.