Question

Which of the following equations has the solution x=
all real numbers?
a. 5(3-x)+7x=3x10-x
b.5(3-x)+7x=3x+15-x
c.5(3-x)+6x=3x+15+2x
d.5(3-x)+7x=x+15-3x

Answer 1

Answer: b.

Work:
- Simplify left side: 5(3−x)+7x = 15 −5x +7x = 15 +2x.

a) Right: 3x+10−x = 2x+10 → 15+2x = 2x+10 ⇒ 15=10 (false) → no solution.
b) Right: 3x+15−x = 2x+15 → 15+2x = 2x+15 ⇒ identity (true for all x).
c) Right: 3x+15+2x = 5x+15 → 15+x = 5x+15 ⇒ x=0 (one solution).
d) Right: x+15−3x = 15−2x → 15+2x = 15−2x ⇒ x=0 (one solution).

Thus option b is true for all real x.