Question

Solve the following inequality for x:
2x2– 2 ≤ 3x

Answer 1

x ∈
`[-(1)/(2),2]`

Explanation:

Answer 2

let's solve for x :

• 
  `2 {x}^(2) - 2 \leqslant 3x`

• 
  `2 {x}^(2) - 3x - 2 \leqslant 0`

• 
  `2 {x}^(2) - 4x + x - 2 \leqslant 0`

• 
  `2x(x - 2) + 1(x - 2) \leqslant 0`

• 
  `(2x + 1)(x - 2) \leqslant 0`

Case 1 :

• 
  `(2x + 1) \leqslant 0`

• 
  `2x \leqslant - 1`

• 
  `x \leqslant - ( 1)/(2)`

Case 2 :

• 
  `x - 2 \leqslant 0`

• 
  `x \leqslant 2`

combining both inequalities we get :

• 
  `x \leqslant - (1)/(2)`