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

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

Step 1

Simplify the first inequality.

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

Add $6$ to both sides of the inequality.

$2 x \geq 2 + 6$ and $2 x - 6 > 14$

Add $2$ and $6$ .

$2 x \geq 8$ and $2 x - 6 > 14$

Divide each term in $2 x \geq 8$ by $2$ and simplify.

Divide each term in $2 x \geq 8$ by $2$ .

$\frac{2 x}{2} \geq \frac{8}{2}$ and $2 x - 6 > 14$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \geq \frac{8}{2}$ and $2 x - 6 > 14$

Divide $x$ by $1$ .

$x \geq \frac{8}{2}$ and $2 x - 6 > 14$

Simplify the right side.

Divide $8$ by $2$ .

$x \geq 4$ and $2 x - 6 > 14$

Step 2

Simplify the second inequality.

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

Add $6$ to both sides of the inequality.

$x \geq 4$ and $2 x > 14 + 6$

Add $14$ and $6$ .

$x \geq 4$ and $2 x > 20$

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

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

$x \geq 4$ and $\frac{2 x}{2} > \frac{20}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$x \geq 4$ and $\frac{2 x}{2} > \frac{20}{2}$

Divide $x$ by $1$ .

$x \geq 4$ and $x > \frac{20}{2}$

Simplify the right side.

Divide $20$ by $2$ .

$x \geq 4$ and $x > 10$

Step 3

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

$x > 10$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > 10$

Interval Notation:

$(10, \infty)$

Step 5

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

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