Algebra Examples

$4 x - 11 \geq 13$ or $4 x + 5 \leq 6$

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 $11$ to both sides of the inequality.

$4 x \geq 13 + 11$

Step 1.1.2

Add $13$ and $11$ .

$4 x \geq 24$

Step 1.2

Divide each term in $4 x \geq 24$ by $4$ and simplify.

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Step 1.2.1

Divide each term in $4 x \geq 24$ by $4$ .

$\frac{4 x}{4} \geq \frac{24}{4}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} \geq \frac{24}{4}$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{24}{4}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $24$ by $4$ .

$x \geq 6$

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

Subtract $5$ from both sides of the inequality.

$4 x \leq 6 - 5$

Step 2.1.2

Subtract $5$ from $6$ .

$4 x \leq 1$

Step 2.2

Divide each term in $4 x \leq 1$ by $4$ and simplify.

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Step 2.2.1

Divide each term in $4 x \leq 1$ by $4$ .

$\frac{4 x}{4} \leq \frac{1}{4}$

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.

$\frac{4 x}{4} \leq \frac{1}{4}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{1}{4}$

Step 3

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

$x \leq \frac{1}{4}$ or $x \geq 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{1}{4} or x \geq 6$

Interval Notation:

$(- \infty, \frac{1}{4}] \cup [6, \infty)$

Step 5