Question

When you solve the equation x + 1 = 2x for x, the solution is 1. 1) Square both sides of the equation, and verify that your solution satisfies the new equation. 2) Show that −13 satisfies the new equation but not the original equation.

Answer 1

(x + 1)² = (2x)²

(1 + 1)² = (2(1))²

2² = 2²

4 = 4

(-1 + 1)² = (2(-13))²

(-12)² = (-26)²

Not true

x = -13 satisfies neither

Answer 2

(x + 1)² = (2x)²

(1 + 1)² = (2(1))²

2² = 2²

4 = 4

(-1 + 1)² = (2(-13))²

(-12)² = (-26)²

Not true

x = -13 satisfies neither