Solve the System of Inequalities -3x+5<=2 or 2x+9<3

$- 3 x + 5 \leq 2$ or $2 x + 9 < 3$

Step 1

Simplify the first inequality.

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

Subtract $5$ from both sides of the inequality.

$- 3 x \leq 2 - 5$ or $2 x + 9 < 3$

Subtract $5$ from $2$ .

$- 3 x \leq - 3$ or $2 x + 9 < 3$

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

Divide each term in $- 3 x \leq - 3$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} \geq \frac{- 3}{- 3}$ or $2 x + 9 < 3$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} \geq \frac{- 3}{- 3}$ or $2 x + 9 < 3$

Divide $x$ by $1$ .

$x \geq \frac{- 3}{- 3}$ or $2 x + 9 < 3$

Simplify the right side.

Divide $- 3$ by $- 3$ .

$x \geq 1$ or $2 x + 9 < 3$

Step 2

Simplify the second inequality.

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

Subtract $9$ from both sides of the inequality.

$x \geq 1$ or $2 x < 3 - 9$

Subtract $9$ from $3$ .

$x \geq 1$ or $2 x < - 6$

Divide each term in $2 x < - 6$ by $2$ and simplify.

Divide each term in $2 x < - 6$ by $2$ .

$x \geq 1$ or $\frac{2 x}{2} < \frac{- 6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$x \geq 1$ or $\frac{2 x}{2} < \frac{- 6}{2}$

Divide $x$ by $1$ .

$x \geq 1$ or $x < \frac{- 6}{2}$

Simplify the right side.

Divide $- 6$ by $2$ .

$x \geq 1$ or $x < - 3$

Step 3

The union consists of all of the elements that are contained in each interval.

$x < - 3$ or $x \geq 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < - 3 or x \geq 1$

Interval Notation:

$(- \infty, - 3) \cup [1, \infty)$

Step 5

Solve the System of Inequalities -3x+5<=2 or 2x+9<3

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