Solve for x 4<3x-2<10

$4 < 3 x - 2 < 10$

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

Add $2$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$4 + 2 < 3 x < 10 + 2$

Add $4$ and $2$ .

$6 < 3 x < 10 + 2$

Add $10$ and $2$ .

$6 < 3 x < 12$

Divide each term in the inequality by $3$ .

$\frac{6}{3} < \frac{3 x}{3} < \frac{12}{3}$

Divide $6$ by $3$ .

$2 < \frac{3 x}{3} < \frac{12}{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$2 < \frac{3 x}{3} < \frac{12}{3}$

Divide $x$ by $1$ .

$2 < x < \frac{12}{3}$

Divide $12$ by $3$ .

$2 < x < 4$

The result can be shown in multiple forms.

Inequality Form:

$2 < x < 4$

Interval Notation:

$(2, 4)$