Algebra Examples

$- 21 < 3 x + 3$ or $27 \geq 3 x + 3$

Step 1

Simplify the first inequality.

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Step 1.1

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

$3 x + 3 > - 21$ or $27 \geq 3 x + 3$

Step 1.2

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

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Step 1.2.1

Subtract $3$ from both sides of the inequality.

$3 x > - 21 - 3$ or $27 \geq 3 x + 3$

Step 1.2.2

Subtract $3$ from $- 21$ .

$3 x > - 24$ or $27 \geq 3 x + 3$

Step 1.3

Divide each term in $3 x > - 24$ by $3$ and simplify.

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Step 1.3.1

Divide each term in $3 x > - 24$ by $3$ .

$\frac{3 x}{3} > \frac{- 24}{3}$ or $27 \geq 3 x + 3$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $3$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} > \frac{- 24}{3}$ or $27 \geq 3 x + 3$

Step 1.3.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 24}{3}$ or $27 \geq 3 x + 3$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Divide $- 24$ by $3$ .

$x > - 8$ or $27 \geq 3 x + 3$

Step 2

Simplify the second inequality.

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Step 2.1

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

$x > - 8$ or $3 x + 3 \leq 27$

Step 2.2

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

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Step 2.2.1

Subtract $3$ from both sides of the inequality.

$x > - 8$ or $3 x \leq 27 - 3$

Step 2.2.2

Subtract $3$ from $27$ .

$x > - 8$ or $3 x \leq 24$

Step 2.3

Divide each term in $3 x \leq 24$ by $3$ and simplify.

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Step 2.3.1

Divide each term in $3 x \leq 24$ by $3$ .

$x > - 8$ or $\frac{3 x}{3} \leq \frac{24}{3}$

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.

$x > - 8$ or $\frac{3 x}{3} \leq \frac{24}{3}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x > - 8$ or $x \leq \frac{24}{3}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $24$ by $3$ .

$x > - 8$ or $x \leq 8$

Step 3

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

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

Step 5