Expert: Scott A Wilson - 10/15/2010

Question
10x-35+3ax=5ax-7a  What number(s) substituted for "a" makes this an identity?  What and how?  Thios is from Algebra I book - a Challenge question in Chapter 3 about solving equations with one variable.  (I know, this one has 2)

Answer
Looking at the equation, divide it into x values and constant values.
This gives 10x + 3ax = 5ax and -35 = -7a.

Taking the 1st eqaution and subtract 3ax from both sides gives
10x = 2ax.  This can be divided by 2x and gives 5 = a.

Using the 2nd equatio to check a = 5, we have -35 = -7*5,
and -7*5 = -35, so it checks.