Algebra Examples

$x + 1 \geq 3$ or $\frac{4}{3} x < - 8$

Step 1

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

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Step 1.1

Subtract $1$ from both sides of the inequality.

$x \geq 3 - 1$ or $\frac{4}{3} x < - 8$

Step 1.2

Subtract $1$ from $3$ .

$x \geq 2$ or $\frac{4}{3} x < - 8$

Step 2

Multiply each term in $\frac{4}{3} x < - 8$ by $\frac{3}{4}$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{4}{3} x < - 8$ by $\frac{3}{4}$ .

$x \geq 2$ or $\frac{4}{3} \cdot (x (\frac{3}{4})) < - 8 (\frac{3}{4})$

Step 2.2

Simplify the left side.

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Step 2.2.1

Combine $\frac{4}{3}$ and $x$ .

$x \geq 2$ or $\frac{4 x}{3} \cdot \frac{3}{4} < - 8 (\frac{3}{4})$

Step 2.2.2

Cancel the common factor of $4$ .

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Step 2.2.2.1

Factor $4$ out of $4 x$ .

$x \geq 2$ or $\frac{4 (x)}{3} \cdot \frac{3}{4} < - 8 (\frac{3}{4})$

Step 2.2.2.2

Cancel the common factor.

$x \geq 2$ or $\frac{4 x}{3} \cdot \frac{3}{4} < - 8 (\frac{3}{4})$

Step 2.2.2.3

Rewrite the expression.

$x \geq 2$ or $\frac{x}{3} \cdot 3 < - 8 (\frac{3}{4})$

Step 2.2.3

Cancel the common factor of $3$ .

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Step 2.2.3.1

Cancel the common factor.

$x \geq 2$ or $\frac{x}{3} \cdot 3 < - 8 (\frac{3}{4})$

Step 2.2.3.2

Rewrite the expression.

$x \geq 2$ or $x < - 8 (\frac{3}{4})$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $4$ .

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Step 2.3.1.1

Factor $4$ out of $- 8$ .

$x \geq 2$ or $x < 4 (- 2) (\frac{3}{4})$

Step 2.3.1.2

Cancel the common factor.

$x \geq 2$ or $x < 4 \cdot (- 2 (\frac{3}{4}))$

Step 2.3.1.3

Rewrite the expression.

$x \geq 2$ or $x < - 2 \cdot 3$

Step 2.3.2

Multiply $- 2$ by $3$ .

$x \geq 2$ or $x < - 6$

Step 3

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

$x < - 6$ or $x \geq 2$

Step 4

Convert the inequality to interval notation.

$(- \infty, - 6) \cup [2, \infty)$

Step 5