Solve for x 3>1-x/2>-3

$3 > 1 - \frac{x}{2} > - 3$

Step 1

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

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

$3 - 1 > - \frac{x}{2} > - 3 - 1$

Subtract $1$ from $3$ .

$2 > - \frac{x}{2} > - 3 - 1$

Multiply each term in the inequality by $2$ .

$2 \cdot 2 > - \frac{x}{2} \cdot 2 > - 3 \cdot 2 - 1 \cdot 2$

Multiply $2$ by $2$ .

$4 > - \frac{x}{2} \cdot 2 > - 3 \cdot 2 - 1 \cdot 2$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$4 > \frac{- x}{2} \cdot 2 > - 3 \cdot 2 - 1 \cdot 2$

Cancel the common factor.

$4 > \frac{- x}{2} \cdot 2 > - 3 \cdot 2 - 1 \cdot 2$

Rewrite the expression.

$4 > - x > - 3 \cdot 2 - 1 \cdot 2$

Simplify each term.

Multiply $- 3$ by $2$ .

$4 > - x > - 6 - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$4 > - x > - 6 - 2$

Subtract $2$ from $- 6$ .

$4 > - x > - 8$

Step 2

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

$\frac{4}{- 1} < \frac{- x}{- 1} < \frac{- 8}{- 1}$

Step 3

Divide $4$ by $- 1$ .

$- 4 < \frac{- x}{- 1} < \frac{- 8}{- 1}$

Step 4

Dividing two negative values results in a positive value.

$- 4 < \frac{x}{1} < \frac{- 8}{- 1}$

Step 5

Divide $x$ by $1$ .

$- 4 < x < \frac{- 8}{- 1}$

Step 6

Divide $- 8$ by $- 1$ .

$- 4 < x < 8$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 4 < x < 8$

Interval Notation:

$(- 4, 8)$

Step 8

Solve for x 3>1-x/2>-3

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