Solve the System of Inequalities 2x<10 or x/2>=3

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

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

Divide each term in $2 x < 10$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $10$ by $2$ .

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

Simplify the second inequality.

Multiply both sides by $2$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$x < 5$ or $x \geq 3 \cdot 2$

Simplify the right side.

Multiply $3$ by $2$ .

$x < 5$ or $x \geq 6$

The result can be shown in multiple forms.

Inequality Form:

$x < 5 or x \geq 6$

Interval Notation:

$(- \infty, 5) \cup [6, \infty)$