Question

For each equation, decide it it is always true, sometimes true or never true.
*
4 points
1. Always True 1. Sometimes True 1. Never True
2x - 10 = x + 1
x - 10 = 2(x - 5) - x
2(x + 3) = 5x + 6 - 3x
x + 1/2 = x - 1/2

Answer 1

1) 2x - 10 = x + 1 — Sometimes true. Solve: x = 11 (true only for that x).

2) x - 10 = 2(x - 5) - x — Always true. RHS = 2x - 10 - x = x - 10, so identity for all x.

3) 2(x + 3) = 5x + 6 - 3x — Always true. LHS = 2x + 6, RHS = (5x - 3x) + 6 = 2x + 6, identity for all x.

4) x + 1/2 = x - 1/2 — Never true. Subtract x: 1/2 = -1/2, contradiction.