Algebra Examples

$- 3 x - 2 < 0$ or $x - 2 < - 5$

Step 1

Simplify the first inequality.

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Step 1.1

Add $2$ to both sides of the inequality.

$- 3 x < 2$ or $x - 2 < - 5$

Step 1.2

Divide each term in $- 3 x < 2$ by $- 3$ and simplify.

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Step 1.2.1

Divide each term in $- 3 x < 2$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 3$ .

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Step 1.2.2.1.1

Cancel the common factor.

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

Step 1.2.2.1.2

Divide $x$ by $1$ .

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

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Move the negative in front of the fraction.

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

Step 2

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

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Step 2.1

Add $2$ to both sides of the inequality.

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

Step 2.2

Add $- 5$ and $2$ .

$x > - \frac{2}{3}$ or $x < - 3$

Step 3

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

$x < - 3$ or $x > - \frac{2}{3}$

Step 4

Convert the inequality to interval notation.

$(- \infty, - 3) \cup (- \frac{2}{3}, \infty)$

Step 5