Solve for x -2<4x-10<6

$- 2 < 4 x - 10 < 6$

Step 1

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

Add $10$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 2 + 10 < 4 x < 6 + 10$

Add $- 2$ and $10$ .

$8 < 4 x < 6 + 10$

Add $6$ and $10$ .

$8 < 4 x < 16$

Step 2

Divide each term in the inequality by $4$ .

$\frac{8}{4} < \frac{4 x}{4} < \frac{16}{4}$

Step 3

Divide $8$ by $4$ .

$2 < \frac{4 x}{4} < \frac{16}{4}$

Step 4

Cancel the common factor of $4$ .

Cancel the common factor.

$2 < \frac{4 x}{4} < \frac{16}{4}$

Divide $x$ by $1$ .

$2 < x < \frac{16}{4}$

Step 5

Divide $16$ by $4$ .

$2 < x < 4$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$2 < x < 4$

Interval Notation:

$(2, 4)$

Step 7