Solve for x -4<=2x+3<=15

$- 4 \leq 2 x + 3 \leq 15$

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.

$- 4 - 3 \leq 2 x \leq 15 - 3$

Subtract $3$ from $- 4$ .

$- 7 \leq 2 x \leq 15 - 3$

Subtract $3$ from $15$ .

$- 7 \leq 2 x \leq 12$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 7}{2} \leq \frac{2 x}{2} \leq \frac{12}{2}$

Step 3

Move the negative in front of the fraction.

$- \frac{7}{2} \leq \frac{2 x}{2} \leq \frac{12}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{7}{2} \leq \frac{2 x}{2} \leq \frac{12}{2}$

Divide $x$ by $1$ .

$- \frac{7}{2} \leq x \leq \frac{12}{2}$

Step 5

Divide $12$ by $2$ .

$- \frac{7}{2} \leq x \leq 6$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- \frac{7}{2} \leq x \leq 6$

Interval Notation:

$[- \frac{7}{2}, 6]$

Step 7