how do i identify the solution set for the inequality:x^2+2x≤3?
is it:
[A] x≤-3 or x≥1
[B] -1≤x≤3
[C] x≤-1 or x≥3
[D] none of these.
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is it:
[A] x≤-3 or x≥1
[B] -1≤x≤3
[C] x≤-1 or x≥3
[D] none of these.
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Verified answer
x² + 2x ≤ 3
∴ x² + 2x - 3 ≤ 0
∴ (x - 1)(x + 3) ≤ 0
Thus one of the factors must be ≤ 0 and the other must be ≥ 0.
x - 1 ≥ 0 and x + 3 ≤ 0 is impossible, so we must have x - 1 ≤ 0 and x + 3 ≥ 0.
∴ x ≤ 1 and x ≥ -3.
∴ -3 ≤ x ≤ 1.
So the answer is D.