Chapter A.9, Problem 77AYU

To determine

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

Answer to Problem 77AYU

$\left\{x|-\infty < x < - 5\right\}$ or $\left(-\infty , - 5\right)$

Explanation of Solution

Given:

$\left(x + 2\right)\left(x - 3\right) > \left(x - 1\right)\left(x + 1\right)$

Calculation:

$\left(x + 2\right)\left(x - 3\right) > \left(x - 1\right)\left(x + 1\right)$

$x^2 - 3x + 2x - 6 > x^2 + x - x - 1$

$x^2 - x - 6 > x^2 - 1$

$x^2 - x - 6 - x^2 + 6 > x^2 - 1 - x^2 + 6$

$- x > 5$

$x < - 5$

The solution set is $\left\{x|-\infty < x < - 5\right\}$ or using interval notation, all numbers in the interval $\left(-\infty , - 5\right)$