Solve the System of Inequalities 2x+8<=6 or 16<2x+8

$2 x + 8 \leq 6$ or $16 < 2 x + 8$

Step 1

Simplify the first inequality.

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

Subtract $8$ from both sides of the inequality.

$2 x \leq 6 - 8$ or $16 < 2 x + 8$

Subtract $8$ from $6$ .

$2 x \leq - 2$ or $16 < 2 x + 8$

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

Divide each term in $2 x \leq - 2$ by $2$ .

$\frac{2 x}{2} \leq \frac{- 2}{2}$ or $16 < 2 x + 8$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{- 2}{2}$ or $16 < 2 x + 8$

Divide $x$ by $1$ .

$x \leq \frac{- 2}{2}$ or $16 < 2 x + 8$

Simplify the right side.

Divide $- 2$ by $2$ .

$x \leq - 1$ or $16 < 2 x + 8$

Step 2

Simplify the second inequality.

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

$x \leq - 1$ or $2 x + 8 > 16$

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

Subtract $8$ from both sides of the inequality.

$x \leq - 1$ or $2 x > 16 - 8$

Subtract $8$ from $16$ .

$x \leq - 1$ or $2 x > 8$

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

Divide each term in $2 x > 8$ by $2$ .

$x \leq - 1$ or $\frac{2 x}{2} > \frac{8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$x \leq - 1$ or $\frac{2 x}{2} > \frac{8}{2}$

Divide $x$ by $1$ .

$x \leq - 1$ or $x > \frac{8}{2}$

Simplify the right side.

Divide $8$ by $2$ .

$x \leq - 1$ or $x > 4$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 1 or x > 4$

Interval Notation:

$(- \infty, - 1] \cup (4, \infty)$

Step 4

Solve the System of Inequalities 2x+8<=6 or 16<2x+8

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