Question

If a(x + 1) + b(x − 1) − 2 = 0 for all real x, then a =

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2

Answer 1

D) 1

Explanation:

using the distributive property we have ax+a+bx-b-2=0. because the equation is true for all real x, ax=-bx. this means a-b-2=0 and a=-b. a-b-2=0 becomes a=b+2. then we substitute a for -b and get -b=b+2 which becomes 2b=-2 so b=-1. since a=-b, a=1