Solve for x -4<2-x<6

$- 4 < 2 - x < 6$

Step 1

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

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

$- 4 - 2 < - x < 6 - 2$

Subtract $2$ from $- 4$ .

$- 6 < - x < 6 - 2$

Subtract $2$ from $6$ .

$- 6 < - x < 4$

Step 2

Multiply each term in the inequality by $- 1$ .

$\frac{- 6}{- 1} > \frac{- x}{- 1} > \frac{4}{- 1}$

Step 3

Divide $- 6$ by $- 1$ .

$6 > \frac{- x}{- 1} > \frac{4}{- 1}$

Step 4

Dividing two negative values results in a positive value.

$6 > \frac{x}{1} > \frac{4}{- 1}$

Step 5

Divide $x$ by $1$ .

$6 > x > \frac{4}{- 1}$

Step 6

Divide $4$ by $- 1$ .

$6 > x > - 4$

Step 7

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- 4 < x < 6$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$- 4 < x < 6$

Interval Notation:

$(- 4, 6)$

Step 9