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Chapter 2: Problem 37

Each number below is a possible solution for \(2 x^2-3 \leq\) \(15-x\) EXCEPT A. -3 B. 0 C. 1 D. 3

Short Answer

Expert verified
The correct answer is D) 3, as it does NOT satisfy the inequality \(2x^2 + x - 18 \leq 0\).

Step by step solution

01

Simplify the inequality

First, subtract the right side of the inequality from the left side to get the whole inequality equal to zero: \[2x^2 - 3 - 15 + x \leq 0\] Simplify further: \[2x^2 + x - 18 \leq 0\] Step 2: Test each option
02

Test each option

Now, test each of the given options in the simplified inequality to see which one(s) do not satisfy the inequality. A) x = -3: \[2(-3)^2 + (-3) - 18 = 2(9) - 3 - 18 = 18 - 3 - 18 = -3\] \(-3 \leq 0\), therefore option A satisfies the inequality. B) x = 0: \[2(0)^2 + 0 - 18 = -18\] \(-18 \leq 0\), therefore option B satisfies the inequality. C) x = 1: \[2(1)^2 + 1 - 18 = 2 + 1 - 18 = -15\] \(-15 \leq 0\), therefore option C satisfies the inequality. D) x = 3: \[2(3)^2 + 3 - 18 = 2(9) + 3 - 18 = 18 + 3 - 18 = 3\] \(3 \nleq 0\), therefore option D does NOT satisfy the inequality. The correct answer is D) 3.

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