Algebra Examples

$- 3 x - 4 \leq - 10$ or $- 16 \geq - 3 x - 4$

Step 1

Simplify the first inequality.

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Step 1.1

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

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Step 1.1.1

Add $4$ to both sides of the inequality.

$- 3 x \leq - 10 + 4$

Step 1.1.2

Add $- 10$ and $4$ .

$- 3 x \leq - 6$

Step 1.2

Divide each term in $- 3 x \leq - 6$ by $- 3$ and simplify.

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Step 1.2.1

Divide each term in $- 3 x \leq - 6$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} \geq \frac{- 6}{- 3}$

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.

$\frac{- 3 x}{- 3} \geq \frac{- 6}{- 3}$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{- 6}{- 3}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $- 6$ by $- 3$ .

$x \geq 2$

Step 2

Simplify the second inequality.

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Step 2.1

Rewrite so $x$ is on the left side of the inequality.

$- 3 x - 4 \leq - 16$

Step 2.2

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

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Step 2.2.1

Add $4$ to both sides of the inequality.

$- 3 x \leq - 16 + 4$

Step 2.2.2

Add $- 16$ and $4$ .

$- 3 x \leq - 12$

Step 2.3

Divide each term in $- 3 x \leq - 12$ by $- 3$ and simplify.

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Step 2.3.1

Divide each term in $- 3 x \leq - 12$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} \geq \frac{- 12}{- 3}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 3$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} \geq \frac{- 12}{- 3}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{- 12}{- 3}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $- 12$ by $- 3$ .

$x \geq 4$

Step 3

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

$x \geq 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq 2$

Interval Notation:

$[2, \infty)$

Step 5