First slide

Introduction to linear inequalities

Question

Which of the following values of x does not satisfy $\frac{5 x + 1}{(x + 1)^{2}} < 1 ?$

Moderate

A

$x < 0$
B

$x > 3$
C

$x > 2$
D

R

Solution

$\begin{array}{l} \frac{5 x + 1}{(x + 1)^{2}} - 1 < 0 \\ \Rightarrow \frac{5 x + 1 - (x + 1)^{2}}{(x + 1)^{2}} < 0 \\ \Rightarrow \frac{- x^{2} + 3 x}{(x + 1)^{2}} < 0 \\ \Rightarrow \frac{x (x - 3)}{(x + 1)^{2}} > 0 \\ \Rightarrow x < 0 or x > 3, x \neq - 1 \end{array}$

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