Solve for x -7<=4x+1<5

$- 7 \leq 4 x + 1 < 5$

Move all terms not containing $x$ from the center section of the inequality.

Subtract $1$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 7 - 1 \leq 4 x < 5 - 1$

Subtract $1$ from $- 7$ .

$- 8 \leq 4 x < 5 - 1$

Subtract $1$ from $5$ .

$- 8 \leq 4 x < 4$

Divide each term in the inequality by $4$ .

$\frac{- 8}{4} \leq \frac{4 x}{4} < \frac{4}{4}$

Divide $- 8$ by $4$ .

$- 2 \leq \frac{4 x}{4} < \frac{4}{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$- 2 \leq \frac{4 x}{4} < \frac{4}{4}$

Divide $x$ by $1$ .

$- 2 \leq x < \frac{4}{4}$

Divide $4$ by $4$ .

$- 2 \leq x < 1$

The result can be shown in multiple forms.

Inequality Form:

$- 2 \leq x < 1$

Interval Notation:

$[- 2, 1)$