Chapter 1.9, Problem 32E

Solution

Solve the inequality $x^2-4x>12$ using the table.

The solution for the inequality is $0<x<8$ .

Given:

The inequality is $x^2-4x>12$ .

Calculation:

Re-write the inequality $x^2-4x>12$ as $x^2-4x-12>0$ .

Construct the table for the inequality $x^2-10x+16<0$ .

$x$	$-1$	$0$	$1$	$-2$	$4$	$6$	$8$	$10$	$12$
$x^2-4x-12$	$27$	$16$	$7$	$0$	$-8$	$0$	$0$	$16$	$40$

From the table, it can be concluded that the value of $x^2-10x+16<0$ for all $x\in \left(0,8\right)$ .

Hence, the required solution for the inequality is $0<x<8$ .