Answer
(-$\infty$, -7/2) U (-1/2,$\infty$)
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
2x+4$\gt$3 and 2x+4$\lt$-3
2.) Solve the first inequality for x by subtracting 4 and dividing by 2 to both sides
2x+4$\gt$3
-4 -4
2x$\gt$-1
$\div$2 $\div$2
x$\gt$-1/2
3.) Identify the interval of x values the inequality is identifying
x$\gt$-1/2 = (-1/2,$\infty$)
4.) Solve the second inequality for x by subtracting 4 and dividing by 2 to both sides
2x+4$\lt$-3
-4 -4
2x$\lt$-7
$\div$2 $\div$2
x$\lt$-7/2
5.) Identify the interval of x values the inequality is identifying
x$\lt$-7/2 = (-$\infty$, -7/2)
6.)Combine the two intervals using a union.
(-$\infty$, -7/2) U (-1/2,$\infty$)
