Solve the System of Inequalities 3x+10<3 or 2x-5>=5

$3 x + 10 < 3$ or $2 x - 5 \geq 5$

Simplify the first inequality.

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

Subtract $10$ from both sides of the inequality.

$3 x < 3 - 10$ or $2 x - 5 \geq 5$

Subtract $10$ from $3$ .

$3 x < - 7$ or $2 x - 5 \geq 5$

Divide each term in $3 x < - 7$ by $3$ and simplify.

Divide each term in $3 x < - 7$ by $3$ .

$\frac{3 x}{3} < \frac{- 7}{3}$ or $2 x - 5 \geq 5$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} < \frac{- 7}{3}$ or $2 x - 5 \geq 5$

Divide $x$ by $1$ .

$x < \frac{- 7}{3}$ or $2 x - 5 \geq 5$

Simplify the right side.

Move the negative in front of the fraction.

$x < - \frac{7}{3}$ or $2 x - 5 \geq 5$

Simplify the second inequality.

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

Add $5$ to both sides of the inequality.

$x < - \frac{7}{3}$ or $2 x \geq 5 + 5$

Add $5$ and $5$ .

$x < - \frac{7}{3}$ or $2 x \geq 10$

Divide each term in $2 x \geq 10$ by $2$ and simplify.

Divide each term in $2 x \geq 10$ by $2$ .

$x < - \frac{7}{3}$ or $\frac{2 x}{2} \geq \frac{10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$x < - \frac{7}{3}$ or $\frac{2 x}{2} \geq \frac{10}{2}$

Divide $x$ by $1$ .

$x < - \frac{7}{3}$ or $x \geq \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$x < - \frac{7}{3}$ or $x \geq 5$

The result can be shown in multiple forms.

Inequality Form:

$x < - \frac{7}{3} or x \geq 5$

Interval Notation:

$(- \infty, - \frac{7}{3}) \cup [5, \infty)$