Solve the System of Inequalities -2x+1>3 or -3x+4<=-5

$- 2 x + 1 > 3$ or $- 3 x + 4 \leq - 5$

Step 1

Simplify the first inequality.

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

Subtract $1$ from both sides of the inequality.

$- 2 x > 3 - 1$ or $- 3 x + 4 \leq - 5$

Subtract $1$ from $3$ .

$- 2 x > 2$ or $- 3 x + 4 \leq - 5$

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

Divide each term in $- 2 x > 2$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} < \frac{2}{- 2}$ or $- 3 x + 4 \leq - 5$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} < \frac{2}{- 2}$ or $- 3 x + 4 \leq - 5$

Divide $x$ by $1$ .

$x < \frac{2}{- 2}$ or $- 3 x + 4 \leq - 5$

Simplify the right side.

Divide $2$ by $- 2$ .

$x < - 1$ or $- 3 x + 4 \leq - 5$

Step 2

Simplify the second inequality.

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

Subtract $4$ from both sides of the inequality.

$x < - 1$ or $- 3 x \leq - 5 - 4$

Subtract $4$ from $- 5$ .

$x < - 1$ or $- 3 x \leq - 9$

Divide each term in $- 3 x \leq - 9$ by $- 3$ and simplify.

Divide each term in $- 3 x \leq - 9$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x < - 1$ or $\frac{- 3 x}{- 3} \geq \frac{- 9}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$x < - 1$ or $\frac{- 3 x}{- 3} \geq \frac{- 9}{- 3}$

Divide $x$ by $1$ .

$x < - 1$ or $x \geq \frac{- 9}{- 3}$

Simplify the right side.

Divide $- 9$ by $- 3$ .

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

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < - 1 or x \geq 3$

Interval Notation:

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

Step 4

Solve the System of Inequalities -2x+1>3 or -3x+4<=-5

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