Algebra Examples

$3 x + 11 < 3$ or $4 x - 1 \geq 9$

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

Subtract $11$ from both sides of the inequality.

$3 x < 3 - 11$ or $4 x - 1 \geq 9$

Step 1.1.2

Subtract $11$ from $3$ .

$3 x < - 8$ or $4 x - 1 \geq 9$

Step 1.2

Divide each term in $3 x < - 8$ by $3$ and simplify.

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Step 1.2.1

Divide each term in $3 x < - 8$ by $3$ .

$\frac{3 x}{3} < \frac{- 8}{3}$ or $4 x - 1 \geq 9$

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.

$\frac{3 x}{3} < \frac{- 8}{3}$ or $4 x - 1 \geq 9$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x < \frac{- 8}{3}$ or $4 x - 1 \geq 9$

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.

$x < - \frac{8}{3}$ or $4 x - 1 \geq 9$

Step 2

Simplify the second inequality.

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Step 2.1

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

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Step 2.1.1

Add $1$ to both sides of the inequality.

$x < - \frac{8}{3}$ or $4 x \geq 9 + 1$

Step 2.1.2

Add $9$ and $1$ .

$x < - \frac{8}{3}$ or $4 x \geq 10$

Step 2.2

Divide each term in $4 x \geq 10$ by $4$ and simplify.

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Step 2.2.1

Divide each term in $4 x \geq 10$ by $4$ .

$x < - \frac{8}{3}$ or $\frac{4 x}{4} \geq \frac{10}{4}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $4$ .

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Step 2.2.2.1.1

Cancel the common factor.

$x < - \frac{8}{3}$ or $\frac{4 x}{4} \geq \frac{10}{4}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x < - \frac{8}{3}$ or $x \geq \frac{10}{4}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Cancel the common factor of $10$ and $4$ .

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Step 2.2.3.1.1

Factor $2$ out of $10$ .

$x < - \frac{8}{3}$ or $x \geq \frac{2 (5)}{4}$

Step 2.2.3.1.2

Cancel the common factors.

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Step 2.2.3.1.2.1

Factor $2$ out of $4$ .

$x < - \frac{8}{3}$ or $x \geq \frac{2 \cdot 5}{2 \cdot 2}$

Step 2.2.3.1.2.2

Cancel the common factor.

$x < - \frac{8}{3}$ or $x \geq \frac{2 \cdot 5}{2 \cdot 2}$

Step 2.2.3.1.2.3

Rewrite the expression.

$x < - \frac{8}{3}$ or $x \geq \frac{5}{2}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < - \frac{8}{3} or x \geq \frac{5}{2}$

Interval Notation:

$(- \infty, - \frac{8}{3}) \cup [\frac{5}{2}, \infty)$

Step 4