Solve for x -19<3x-5<1

$- 19 < 3 x - 5 < 1$

Step 1

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

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

$- 19 + 5 < 3 x < 1 + 5$

Add $- 19$ and $5$ .

$- 14 < 3 x < 1 + 5$

Add $1$ and $5$ .

$- 14 < 3 x < 6$

Step 2

Divide each term in the inequality by $3$ .

$\frac{- 14}{3} < \frac{3 x}{3} < \frac{6}{3}$

Step 3

Move the negative in front of the fraction.

$- \frac{14}{3} < \frac{3 x}{3} < \frac{6}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$- \frac{14}{3} < \frac{3 x}{3} < \frac{6}{3}$

Divide $x$ by $1$ .

$- \frac{14}{3} < x < \frac{6}{3}$

Step 5

Divide $6$ by $3$ .

$- \frac{14}{3} < x < 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- \frac{14}{3} < x < 2$

Interval Notation:

$(- \frac{14}{3}, 2)$

Step 7