Solve for x 5<3x-1<14

$5 < 3 x - 1 < 14$

Step 1

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

Add $1$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$5 + 1 < 3 x < 14 + 1$

Add $5$ and $1$ .

$6 < 3 x < 14 + 1$

Add $14$ and $1$ .

$6 < 3 x < 15$

Step 2

Divide each term in the inequality by $3$ .

$\frac{6}{3} < \frac{3 x}{3} < \frac{15}{3}$

Step 3

Divide $6$ by $3$ .

$2 < \frac{3 x}{3} < \frac{15}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$2 < \frac{3 x}{3} < \frac{15}{3}$

Divide $x$ by $1$ .

$2 < x < \frac{15}{3}$

Step 5

Divide $15$ by $3$ .

$2 < x < 5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$2 < x < 5$

Interval Notation:

$(2, 5)$

Step 7