Question

Solve for x
𝑥
to determine if the equation has one, none, or infinite solutions.
11x=3(7x−1)−10x
11
𝑥
=
3
(
7
𝑥
−
1
)
−
10
𝑥

Answer 1

Solve: 11x = 3(7x − 1) − 10x

Expand the right side: 3(7x − 1) − 10x = 21x − 3 − 10x = 11x − 3

So the equation becomes 11x = 11x − 3. Subtract 11x from both sides: 0 = −3, which is false.

Therefore the equation is inconsistent and has no solution (solution set = ∅).