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

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

Step 1

Simplify the first inequality.

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

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

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

Subtract $4$ from both sides of the inequality.

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

Subtract $4$ from $2$ .

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

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 2$ by $- 2$ .

$x < 1$ and $- 2 x + 4 > - 14$

Step 2

Simplify the second inequality.

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

Subtract $4$ from both sides of the inequality.

$x < 1$ and $- 2 x > - 14 - 4$

Subtract $4$ from $- 14$ .

$x < 1$ and $- 2 x > - 18$

Divide each term in $- 2 x > - 18$ by $- 2$ and simplify.

Divide each term in $- 2 x > - 18$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x < 1$ and $\frac{- 2 x}{- 2} < \frac{- 18}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$x < 1$ and $\frac{- 2 x}{- 2} < \frac{- 18}{- 2}$

Divide $x$ by $1$ .

$x < 1$ and $x < \frac{- 18}{- 2}$

Simplify the right side.

Divide $- 18$ by $- 2$ .

$x < 1$ and $x < 9$

Step 3

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

$x < 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 1$

Interval Notation:

$(- \infty, 1)$

Step 5

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

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