Question

what is a value of x that satisfies the inequality?
$18 < 2x^2 < 50$
a) $x = 4$
b) $x = 5$
c) $x = 20$
d) $x = 25$

Explanation:

Step1: Simplify the inequality

Divide each part of the inequality \(18 < 2x^{2}<50\) by 2.
We get \( \frac{18}{2}<\frac{2x^{2}}{2}<\frac{50}{2} \), which simplifies to \(9 < x^{2}<25\).

Step2: Analyze each option

• For option A: \(x = 4\), then \(x^{2}=16\). Check if \(9 < 16<25\). Yes, 9 < 16 and 16 < 25.
• For option B: \(x = 5\), then \(x^{2}=25\). But the inequality is \(x^{2}<25\), so 25 is not less than 25. So this does not satisfy.
• For option C: \(x = 20\), then \(x^{2}=400\). 400 is not less than 25, so this does not satisfy.
• For option D: \(x = 25\), then \(x^{2}=625\). 625 is not less than 25, so this does not satisfy.

Answer:

A) \(x = 4\)