Answer
$-\frac{3}{4}\lt x\lt-\frac{1}{4}$
See graph
Work Step by Step
For
$$\frac{3}{4}\gt x+1$$
$$\frac{3}{4}-1\gt x+1-1$$
$$\frac{3-4}{4}\gt x$$
$$-\frac{1}{4}\gt x$$
$$x\lt-\frac{1}{4}$$
For
$$x+1\gt\frac{1}{4}$$
$$x+1-1\gt\frac{1}{4}-1$$
$$x\gt\frac{1-4}{4}$$
$$x\gt-\frac{3}{4}$$
Combining:
$$x\gt-\frac{3}{4}\text{ and }x\lt-\frac{1}{4}$$
$$-\frac{3}{4}\lt x\lt-\frac{1}{4}$$
The graph of the solution set is as shown.
