Solve the System of Inequalities -2x-4>12 and -2x-4>-14

$- 2 x - 4 > 12$ and $- 2 x - 4 > - 14$

Step 1

Simplify the first inequality.

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

Add $4$ to both sides of the inequality.

$- 2 x > 12 + 4$ and $- 2 x - 4 > - 14$

Add $12$ and $4$ .

$- 2 x > 16$ and $- 2 x - 4 > - 14$

Divide each term in $- 2 x > 16$ by $- 2$ and simplify.

Divide each term in $- 2 x > 16$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} < \frac{16}{- 2}$ and $- 2 x - 4 > - 14$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} < \frac{16}{- 2}$ and $- 2 x - 4 > - 14$

Divide $x$ by $1$ .

$x < \frac{16}{- 2}$ and $- 2 x - 4 > - 14$

Simplify the right side.

Divide $16$ by $- 2$ .

$x < - 8$ and $- 2 x - 4 > - 14$

Step 2

Simplify the second inequality.

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

Add $4$ to both sides of the inequality.

$x < - 8$ and $- 2 x > - 14 + 4$

Add $- 14$ and $4$ .

$x < - 8$ and $- 2 x > - 10$

Divide each term in $- 2 x > - 10$ by $- 2$ and simplify.

Divide each term in $- 2 x > - 10$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x < - 8$ and $\frac{- 2 x}{- 2} < \frac{- 10}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$x < - 8$ and $\frac{- 2 x}{- 2} < \frac{- 10}{- 2}$

Divide $x$ by $1$ .

$x < - 8$ and $x < \frac{- 10}{- 2}$

Simplify the right side.

Divide $- 10$ by $- 2$ .

$x < - 8$ and $x < 5$

Step 3

The intersection consists of the elements that are contained in both intervals.

$x < - 8$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < - 8$

Interval Notation:

$(- \infty, - 8)$

Step 5

Solve the System of Inequalities -2x-4>12 and -2x-4>-14

Related Questions

Support LCMGCF.com by disabling your adblocker.