Chapter A.9, Problem 83AYU

To determine

To solve: Each inequality. Express your answer using set notation or interval notation. Graph the solution set.

Answer to Problem 83AYU

$\left\{x|- \infty < x < - \frac{1}{2}\right\}$ or $\left(-\infty , - \frac{1}{2}\right]$

Explanation of Solution

Given:

${\left(4x + 2\right)}^{- 1} < 0$

Calculation:

${\left(4x + 2\right)}^{- 1} < 0$

$\frac{1}{4x + 2} < 0$

$\frac{1}{2\left(2x + 1\right)} < 0$

Multiply by 2

$\frac{1}{2x + 1} < 0$

$2x + 1 < 0$

$2x + 1 - 1 < 0 - 1$

$2x < - 1$

Divide by 2

$x < - \frac{1}{2}$

The solution set is $\left\{x|- \infty < x < - \frac{1}{2}\right\}$ or using interval notation, all numbers in the interval $\left(-\infty , - \frac{1}{2}\right]$.