Solve for x 3<=2x+3<=13

$3 \leq 2 x + 3 \leq 13$

Step 1

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

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

$3 - 3 \leq 2 x \leq 13 - 3$

Subtract $3$ from $3$ .

$0 \leq 2 x \leq 13 - 3$

Subtract $3$ from $13$ .

$0 \leq 2 x \leq 10$

Step 2

Divide each term in the inequality by $2$ .

$\frac{0}{2} \leq \frac{2 x}{2} \leq \frac{10}{2}$

Step 3

Divide $0$ by $2$ .

$0 \leq \frac{2 x}{2} \leq \frac{10}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$0 \leq \frac{2 x}{2} \leq \frac{10}{2}$

Divide $x$ by $1$ .

$0 \leq x \leq \frac{10}{2}$

Step 5

Divide $10$ by $2$ .

$0 \leq x \leq 5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$0 \leq x \leq 5$

Interval Notation:

$[0, 5]$

Step 7