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G(x)=2x²-3x-4.
Solve G(x) ≤ 5.

User Deroccha
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1 Answer

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11 votes

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).

User Jesse Pangburn
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