Convert to Interval Notation -5x-3>=2 or 4x-2>=5

$- 5 x - 3 \geq 2$ or $4 x - 2 \geq 5$

Simplify the first inequality.

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

Add $3$ to both sides of the inequality.

$- 5 x \geq 2 + 3$

Add $2$ and $3$ .

$- 5 x \geq 5$

Divide each term in $- 5 x \geq 5$ by $- 5$ and simplify.

Divide each term in $- 5 x \geq 5$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} \leq \frac{5}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} \leq \frac{5}{- 5}$

Divide $x$ by $1$ .

$x \leq \frac{5}{- 5}$

Simplify the right side.

Divide $5$ by $- 5$ .

$x \leq - 1$

Simplify the second inequality.

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

Add $2$ to both sides of the inequality.

$4 x \geq 5 + 2$

Add $5$ and $2$ .

$4 x \geq 7$

Divide each term in $4 x \geq 7$ by $4$ and simplify.

Divide each term in $4 x \geq 7$ by $4$ .

$\frac{4 x}{4} \geq \frac{7}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} \geq \frac{7}{4}$

Divide $x$ by $1$ .

$x \geq \frac{7}{4}$

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

$x \leq - 1$ or $x \geq \frac{7}{4}$

Convert the inequality to interval notation.

$(- \infty, - 1] \cup [\frac{7}{4}, \infty)$

Convert to Interval Notation -5x-3>=2 or 4x-2>=5

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