Solve for x -5<4x+1<=3

$- 5 < 4 x + 1 \leq 3$

Step 1

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.

$- 5 - 1 < 4 x \leq 3 - 1$

Subtract $1$ from $- 5$ .

$- 6 < 4 x \leq 3 - 1$

Subtract $1$ from $3$ .

$- 6 < 4 x \leq 2$

Step 2

Divide each term in the inequality by $4$ .

$\frac{- 6}{4} < \frac{4 x}{4} \leq \frac{2}{4}$

Step 3

Cancel the common factor of $- 6$ and $4$ .

Factor $2$ out of $- 6$ .

$\frac{2 (- 3)}{4} < \frac{4 x}{4} \leq \frac{2}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{2 \cdot - 3}{2 \cdot 2} < \frac{4 x}{4} \leq \frac{2}{4}$

Cancel the common factor.

$\frac{2 \cdot - 3}{2 \cdot 2} < \frac{4 x}{4} \leq \frac{2}{4}$

Rewrite the expression.

$\frac{- 3}{2} < \frac{4 x}{4} \leq \frac{2}{4}$

Step 4

Move the negative in front of the fraction.

$- \frac{3}{2} < \frac{4 x}{4} \leq \frac{2}{4}$

Step 5

Cancel the common factor of $4$ .

Cancel the common factor.

$- \frac{3}{2} < \frac{4 x}{4} \leq \frac{2}{4}$

Divide $x$ by $1$ .

$- \frac{3}{2} < x \leq \frac{2}{4}$

Step 6

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$- \frac{3}{2} < x \leq \frac{2 (1)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$- \frac{3}{2} < x \leq \frac{2 \cdot 1}{2 \cdot 2}$

Cancel the common factor.

$- \frac{3}{2} < x \leq \frac{2 \cdot 1}{2 \cdot 2}$

Rewrite the expression.

$- \frac{3}{2} < x \leq \frac{1}{2}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- \frac{3}{2} < x \leq \frac{1}{2}$

Interval Notation:

$(- \frac{3}{2}, \frac{1}{2}]$

Step 8

Solve for x -5<4x+1<=3

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