Solve for x -10<3x-4<8

$- 10 < 3 x - 4 < 8$

Step 1

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

Add $4$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 10 + 4 < 3 x < 8 + 4$

Add $- 10$ and $4$ .

$- 6 < 3 x < 8 + 4$

Add $8$ and $4$ .

$- 6 < 3 x < 12$

Step 2

Divide each term in the inequality by $3$ .

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

Step 3

Divide $- 6$ by $3$ .

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

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 5

Divide $12$ by $3$ .

$- 2 < x < 4$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 2 < x < 4$

Interval Notation:

$(- 2, 4)$

Step 7