Solve for x 5<=4x-3<9

$5 \leq 4 x - 3 < 9$

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

Add $3$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$5 + 3 \leq 4 x < 9 + 3$

Add $5$ and $3$ .

$8 \leq 4 x < 9 + 3$

Add $9$ and $3$ .

$8 \leq 4 x < 12$

Divide each term in the inequality by $4$ .

$\frac{8}{4} \leq \frac{4 x}{4} < \frac{12}{4}$

Divide $8$ by $4$ .

$2 \leq \frac{4 x}{4} < \frac{12}{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$2 \leq \frac{4 x}{4} < \frac{12}{4}$

Divide $x$ by $1$ .

$2 \leq x < \frac{12}{4}$

Divide $12$ by $4$ .

$2 \leq x < 3$

The result can be shown in multiple forms.

Inequality Form:

$2 \leq x < 3$

Interval Notation:

$[2, 3)$