Question

Can someone solve this inequality for x
(x–2)a ≤ x+1 if a>1

Answer 1

x ≤ (1+2a) / (a-1) where a > 1

Explanation:

(x–2)a ≤ x+1

x(a) -2(a) ≤ x + 1

ax -2a ≤ x + 1 (subtract x from both sides)

ax -2a - x ≤ 1 (add 2a to both sides)

ax - x ≤ 1 + 2a (factor out x from left side)

x (a - 1) ≤ 1 + 2a

x ≤ (1+2a) / (a-1) where a > 1