Solve the Inequality for x -2<5+3x<20

$- 2 < 5 + 3 x < 20$

Step 1

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

Subtract $5$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 2 - 5 < 3 x < 20 - 5$

Subtract $5$ from $- 2$ .

$- 7 < 3 x < 20 - 5$

Subtract $5$ from $20$ .

$- 7 < 3 x < 15$

Step 2

Divide each term in the inequality by $3$ .

$\frac{- 7}{3} < \frac{3 x}{3} < \frac{15}{3}$

Step 3

Move the negative in front of the fraction.

$- \frac{7}{3} < \frac{3 x}{3} < \frac{15}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$- \frac{7}{3} < \frac{3 x}{3} < \frac{15}{3}$

Divide $x$ by $1$ .

$- \frac{7}{3} < x < \frac{15}{3}$

Step 5

Divide $15$ by $3$ .

$- \frac{7}{3} < x < 5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- \frac{7}{3} < x < 5$

Interval Notation:

$(- \frac{7}{3}, 5)$

Step 7