Algebra Examples

$\frac{k}{4} \geq 1$ or $\frac{k}{3} \leq - 1$

Step 1

Simplify the first inequality.

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Step 1.1

Multiply both sides by $4$ .

$\frac{k}{4} \cdot 4 \geq 1 \cdot 4$

Step 1.2

Simplify.

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Step 1.2.1

Simplify the left side.

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Step 1.2.1.1

Cancel the common factor of $4$ .

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Step 1.2.1.1.1

Cancel the common factor.

$\frac{k}{4} \cdot 4 \geq 1 \cdot 4$

Step 1.2.1.1.2

Rewrite the expression.

$k \geq 1 \cdot 4$

$k \geq 1 \cdot 4$

$k \geq 1 \cdot 4$

Step 1.2.2

Simplify the right side.

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Step 1.2.2.1

Multiply $4$ by $1$ .

$k \geq 4$

$k \geq 4$

$k \geq 4$

$k \geq 4$

Step 2

Simplify the second inequality.

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Step 2.1

Multiply both sides by $3$ .

$\frac{k}{3} \cdot 3 \leq - 1 \cdot 3$

Step 2.2

Simplify.

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Cancel the common factor of $3$ .

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Step 2.2.1.1.1

Cancel the common factor.

$\frac{k}{3} \cdot 3 \leq - 1 \cdot 3$

Step 2.2.1.1.2

Rewrite the expression.

$k \leq - 1 \cdot 3$

$k \leq - 1 \cdot 3$

$k \leq - 1 \cdot 3$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Multiply $- 1$ by $3$ .

$k \leq - 3$

$k \leq - 3$

$k \leq - 3$

$k \leq - 3$

Step 3

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

$k \leq - 3$ or $k \geq 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$k \leq - 3 or k \geq 4$

Interval Notation:

$(- \infty, - 3] \cup [4, \infty)$

Step 5

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$