Solve the System of @WORD 6>1-x/2>-6

$6 > 1 - \frac{x}{2} > - 6$

Step 1

Solve $6 > 1 - \frac{x}{2}$ for $x$ .

Rewrite so $x$ is on the left side of the inequality.

$1 - \frac{x}{2} < 6$

Move all terms not containing $x$ to the right side of the inequality.

Subtract $1$ from both sides of the inequality.

$- \frac{x}{2} < 6 - 1$

Subtract $1$ from $6$ .

$- \frac{x}{2} < 5$

Divide each term in $- \frac{x}{2} < 5$ by $- 1$ and simplify.

Divide each term in $- \frac{x}{2} < 5$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{x}{2}}{- 1} > \frac{5}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{x}{2}}{1} > \frac{5}{- 1}$

Divide $\frac{x}{2}$ by $1$ .

$\frac{x}{2} > \frac{5}{- 1}$

Simplify the right side.

Divide $5$ by $- 1$ .

$\frac{x}{2} > - 5$

Multiply both sides by $2$ .

$\frac{x}{2} \cdot 2 > - 5 \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x}{2} \cdot 2 > - 5 \cdot 2$

Rewrite the expression.

$x > - 5 \cdot 2$

Simplify the right side.

Multiply $- 5$ by $2$ .

$x > - 10$

Step 2

Solve $1 - \frac{x}{2} > - 6$ for $x$ .

Move all terms not containing $x$ to the right side of the inequality.

Subtract $1$ from both sides of the inequality.

$- \frac{x}{2} > - 6 - 1$

Subtract $1$ from $- 6$ .

$- \frac{x}{2} > - 7$

Divide each term in $- \frac{x}{2} > - 7$ by $- 1$ and simplify.

Divide each term in $- \frac{x}{2} > - 7$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $\frac{x}{2}$ by $1$ .

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

Simplify the right side.

Divide $- 7$ by $- 1$ .

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

Multiply both sides by $2$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$x < 7 \cdot 2$

Simplify the right side.

Multiply $7$ by $2$ .

$x < 14$

Step 3

Find the intersection of $x > - 10$ and $x < 14$ .

$- 10 < x < 14$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 10 < x < 14$

Interval Notation:

$(- 10, 14)$

Step 5

Solve the System of @WORD 6>1-x/2>-6

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