Answer:
inequality: -3/2≤x≤3
interval notation: [-3/2,3]
Explanation:
2x²-3x-4 ≤ 5
1. Solve 2x²-3x-4 = 5 to find Boundary Numbers
⇒ 2x²-3x-9 = 0
⇒ (2x+3)(x-3) = 0
⇒ x = -3/2, 3
2. Test numbers in 2x²-3x-4 ≤ 5:
a. smaller than -3/2: 2(-2)²-3(-2)-4 ≤ 5? ⇒ 8+6-4 ≤ 5? FALSE
b. between -3/2 and 3: 2(0)²-3(0)-4 ≤ 5? ⇒ 0-0-4 ≤ 5? TRUE
c. larger than 3: 2(4)²-3(4)-4 ≤ 5? ⇒ 32-12-4 ≤ 5? FALSE
3. The TRUE statement(s) gives you the solution(s).