Solve the System of Inequalities 14>=3x-7 or 3x-7>20

$14 \geq 3 x - 7$ or $3 x - 7 > 20$

Simplify the first inequality.

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

$3 x - 7 \leq 14$ or $3 x - 7 > 20$

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

Add $7$ to both sides of the inequality.

$3 x \leq 14 + 7$ or $3 x - 7 > 20$

Add $14$ and $7$ .

$3 x \leq 21$ or $3 x - 7 > 20$

Divide each term in $3 x \leq 21$ by $3$ and simplify.

Divide each term in $3 x \leq 21$ by $3$ .

$\frac{3 x}{3} \leq \frac{21}{3}$ or $3 x - 7 > 20$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \leq \frac{21}{3}$ or $3 x - 7 > 20$

Divide $x$ by $1$ .

$x \leq \frac{21}{3}$ or $3 x - 7 > 20$

Simplify the right side.

Divide $21$ by $3$ .

$x \leq 7$ or $3 x - 7 > 20$

Simplify the second inequality.

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

Add $7$ to both sides of the inequality.

$x \leq 7$ or $3 x > 20 + 7$

Add $20$ and $7$ .

$x \leq 7$ or $3 x > 27$

Divide each term in $3 x > 27$ by $3$ and simplify.

Divide each term in $3 x > 27$ by $3$ .

$x \leq 7$ or $\frac{3 x}{3} > \frac{27}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$x \leq 7$ or $\frac{3 x}{3} > \frac{27}{3}$

Divide $x$ by $1$ .

$x \leq 7$ or $x > \frac{27}{3}$

Simplify the right side.

Divide $27$ by $3$ .

$x \leq 7$ or $x > 9$

The result can be shown in multiple forms.

Inequality Form:

$x \leq 7 or x > 9$

Interval Notation:

$(- \infty, 7] \cup (9, \infty)$