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What is the solution to the inequality x^2 + 2x ≤ 24?

A)
x < 4 or x > –6

B)
–6 ≤ x ≤ 4

C)
–6 < x < 4

D)
x ≤ –6 or x ≥ 4

User MarkII
by
8.3k points

1 Answer

11 votes

Answer:

B. -6 ≤ x ≤ -4

Explanation:

1. Rewrite the inequality in standard form:

x² + 2x - 24 ≤ 0

2. Factor x² + 2x - 24:

(x-4)(x+6) ≤ 0

3. Identify the intervals:

x - 4+4 = 0+4, x + 6-6 = 0-6

x = 4, x = -6

In conclusion:

-6 ≤ x ≤ -4

hope this helps!

User Hayha
by
8.1k points

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