QuestionApril 20, 2025

Consider the following polynomial inequality: (1)/(2x+5)gt 1 Step 1 of 2:Write the polynomial inequality in the form p(x)lt 0,p(x)leqslant 0,p(x)gt 0,orp(x)geqslant 0 then find the real zeros of p(x)

Consider the following polynomial inequality: (1)/(2x+5)gt 1 Step 1 of 2:Write the polynomial inequality in the form p(x)lt 0,p(x)leqslant 0,p(x)gt 0,orp(x)geqslant 0 then find the real zeros of p(x)
Consider the following polynomial inequality: (1)/(2x+5)gt 1
Step 1 of 2:Write the polynomial inequality in the form p(x)lt 0,p(x)leqslant 0,p(x)gt 0,orp(x)geqslant 0 then find the real zeros of p(x)

Solution
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Answer

p(x) = \frac{-2x-4}{2x+5}, zero at x = -2. Explanation 1. Rewrite the inequality Start with \frac{1}{2x+5} > 1. Subtract 1 from both sides to get \frac{1}{2x+5} - 1 > 0. 2. Simplify the expression Combine into a single fraction: \frac{1 - (2x+5)}{2x+5} > 0, which simplifies to \frac{-2x-4}{2x+5} > 0. 3. Find real zeros of numerator Set -2x-4 = 0. Solve for x: x = -2.

Explanation

1. Rewrite the inequality<br /> Start with $\frac{1}{2x+5} > 1$. Subtract 1 from both sides to get $\frac{1}{2x+5} - 1 > 0$.<br />2. Simplify the expression<br /> Combine into a single fraction: $\frac{1 - (2x+5)}{2x+5} > 0$, which simplifies to $\frac{-2x-4}{2x+5} > 0$.<br />3. Find real zeros of numerator<br /> Set $-2x-4 = 0$. Solve for $x$: $x = -2$.
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