Question

If ax+3=7-bx what is x expressed in terms of a and b

Answer 1

All we want to do is get an equation with just x on one side and no x's on the other.
We can use inverse operations to accomplish this.

First, bring bx to the left side. Subtract the 3.
Factor ax+bx to x(a+b). (this is pretty much reversing the distributive property)
Divide by a+b and you are left with just x on the left side as 4/(a+b).


`ax+3=7-bx \\ ax+bx+3=7-bx+bx\\ax+bx+3=7 \\\\ ax+bx+3-3=7-3\\ax+bx=4 \\\\ x(a+b)=4 \\(x(a+b))/(a+b)=(4)/(a+b)\\\boxed{x=(4)/(a+b)}`