Solve the System of Inequalities -2>2x-6 and 14>2x-6

$- 2 > 2 x - 6$ and $14 > 2 x - 6$

Step 1

Simplify the first inequality.

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

$2 x - 6 < - 2$ and $14 > 2 x - 6$

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

Add $6$ to both sides of the inequality.

$2 x < - 2 + 6$ and $14 > 2 x - 6$

Add $- 2$ and $6$ .

$2 x < 4$ and $14 > 2 x - 6$

Divide each term in $2 x < 4$ by $2$ and simplify.

Divide each term in $2 x < 4$ by $2$ .

$\frac{2 x}{2} < \frac{4}{2}$ and $14 > 2 x - 6$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{4}{2}$ and $14 > 2 x - 6$

Divide $x$ by $1$ .

$x < \frac{4}{2}$ and $14 > 2 x - 6$

Simplify the right side.

Divide $4$ by $2$ .

$x < 2$ and $14 > 2 x - 6$

Step 2

Simplify the second inequality.

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

$x < 2$ and $2 x - 6 < 14$

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

Add $6$ to both sides of the inequality.

$x < 2$ and $2 x < 14 + 6$

Add $14$ and $6$ .

$x < 2$ and $2 x < 20$

Divide each term in $2 x < 20$ by $2$ and simplify.

Divide each term in $2 x < 20$ by $2$ .

$x < 2$ and $\frac{2 x}{2} < \frac{20}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$x < 2$ and $\frac{2 x}{2} < \frac{20}{2}$

Divide $x$ by $1$ .

$x < 2$ and $x < \frac{20}{2}$

Simplify the right side.

Divide $20$ by $2$ .

$x < 2$ and $x < 10$

Step 3

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

$x < 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 2$

Interval Notation:

$(- \infty, 2)$

Step 5

Solve the System of Inequalities -2>2x-6 and 14>2x-6

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