Answer
(-$\infty$,2) U (6,$\infty$)
Work Step by Step
1.) Set what the inequality equals to what it originally equals, and then set it to the opposite of that number with the opposite inequality sign
x-4$\gt$2 and x-4$\lt$-2
2.) Solve the first inequality for x by adding 4 to both sides
x-4$\gt$2
+4 +4
x$\gt$6
3.) Identify the interval of x values the inequality is identifying
x$\gt$6 = (6,$\infty$)
4.) Solve the second inequality for x by adding 4 to both sides
x-4$\lt$-2
+4 +4
x$\lt$2
5.) Identify the interval of x values the inequality is identifying
x$\lt$2 = (-$\infty$,2)
6.)Combine the two intervals using a union.
(-$\infty$,2) U (6,$\infty$)
