Solve for x 6>1-x/2>-6

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

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.

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

Subtract $1$ from $6$ .

$5 > - \frac{x}{2} > - 6 - 1$

Multiply each term in the inequality by $2$ .

$5 \cdot 2 > - \frac{x}{2} \cdot 2 > - 6 \cdot 2 - 1 \cdot 2$

Multiply $5$ by $2$ .

$10 > - \frac{x}{2} \cdot 2 > - 6 \cdot 2 - 1 \cdot 2$

Cancel the common factor of $2$ .

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

$10 > \frac{- x}{2} \cdot 2 > - 6 \cdot 2 - 1 \cdot 2$

Cancel the common factor.

$10 > \frac{- x}{2} \cdot 2 > - 6 \cdot 2 - 1 \cdot 2$

Rewrite the expression.

$10 > - x > - 6 \cdot 2 - 1 \cdot 2$

Simplify each term.

Multiply $- 6$ by $2$ .

$10 > - x > - 12 - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$10 > - x > - 12 - 2$

Subtract $2$ from $- 12$ .

$10 > - x > - 14$

Step 2

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

$\frac{10}{- 1} < \frac{- x}{- 1} < \frac{- 14}{- 1}$

Step 3

Divide $10$ by $- 1$ .

$- 10 < \frac{- x}{- 1} < \frac{- 14}{- 1}$

Step 4

Dividing two negative values results in a positive value.

$- 10 < \frac{x}{1} < \frac{- 14}{- 1}$

Step 5

Divide $x$ by $1$ .

$- 10 < x < \frac{- 14}{- 1}$

Step 6

Divide $- 14$ by $- 1$ .

$- 10 < x < 14$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 10 < x < 14$

Interval Notation:

$(- 10, 14)$

Step 8

Solve for x 6>1-x/2>-6

Related Questions

Support LCMGCF.com by disabling your adblocker.