Convert to Set Notation 0<3-1/2x<7

$0 < 3 - \frac{1}{2} x < 7$

Step 1

Solve $6 > x > - 8$ .

Combine $x$ and $\frac{1}{2}$ .

$0 < 3 - \frac{x}{2} < 7$

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

Subtract $3$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$0 - 3 < - \frac{x}{2} < 7 - 3$

Subtract $3$ from $0$ .

$- 3 < - \frac{x}{2} < 7 - 3$

Multiply each term in the inequality by $2$ .

$- 3 \cdot 2 < - \frac{x}{2} \cdot 2 < 7 \cdot 2 - 3 \cdot 2$

Multiply $- 3$ by $2$ .

$- 6 < - \frac{x}{2} \cdot 2 < 7 \cdot 2 - 3 \cdot 2$

Cancel the common factor of $2$ .

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

$- 6 < \frac{- x}{2} \cdot 2 < 7 \cdot 2 - 3 \cdot 2$

Cancel the common factor.

$- 6 < \frac{- x}{2} \cdot 2 < 7 \cdot 2 - 3 \cdot 2$

Rewrite the expression.

$- 6 < - x < 7 \cdot 2 - 3 \cdot 2$

Simplify each term.

Multiply $7$ by $2$ .

$- 6 < - x < 14 - 3 \cdot 2$

Multiply $- 3$ by $2$ .

$- 6 < - x < 14 - 6$

Subtract $6$ from $14$ .

$- 6 < - x < 8$

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

$\frac{- 6}{- 1} > \frac{- x}{- 1} > \frac{8}{- 1}$

Divide $- 6$ by $- 1$ .

$6 > \frac{- x}{- 1} > \frac{8}{- 1}$

Dividing two negative values results in a positive value.

$6 > \frac{x}{1} > \frac{8}{- 1}$

Divide $x$ by $1$ .

$6 > x > \frac{8}{- 1}$

Divide $8$ by $- 1$ .

$6 > x > - 8$

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

$- 8 < x < 6$

Step 2

Use the inequality $- 8 < x < 6$ to build the set notation.

${x | - 8 < x < 6}$

Step 3