Algebra Examples

$8.6 \leq x - 5 \frac{4}{5}$

Step 1

Simplify the right side.

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Step 1.1

Convert $5 \frac{4}{5}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

$8.6 \leq x - (5 + \frac{4}{5})$

Step 1.1.2

Add $5$ and $\frac{4}{5}$ .

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Step 1.1.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$8.6 \leq x - (5 \cdot \frac{5}{5} + \frac{4}{5})$

Step 1.1.2.2

Combine $5$ and $\frac{5}{5}$ .

$8.6 \leq x - (\frac{5 \cdot 5}{5} + \frac{4}{5})$

Step 1.1.2.3

Combine the numerators over the common denominator.

$8.6 \leq x - \frac{5 \cdot 5 + 4}{5}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $5$ by $5$ .

$8.6 \leq x - \frac{25 + 4}{5}$

Step 1.1.2.4.2

Add $25$ and $4$ .

$8.6 \leq x - \frac{29}{5}$

Step 2

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

$x - \frac{29}{5} \geq 8.6$

Step 3

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

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Step 3.1

Add $\frac{29}{5}$ to both sides of the inequality.

$x \geq 8.6 + \frac{29}{5}$

Step 3.2

To write $8.6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x \geq 8.6 \cdot \frac{5}{5} + \frac{29}{5}$

Step 3.3

Combine $8.6$ and $\frac{5}{5}$ .

$x \geq \frac{8.6 \cdot 5}{5} + \frac{29}{5}$

Step 3.4

Combine the numerators over the common denominator.

$x \geq \frac{8.6 \cdot 5 + 29}{5}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $8.6$ by $5$ .

$x \geq \frac{43 + 29}{5}$

Step 3.5.2

Add $43$ and $29$ .

$x \geq \frac{72}{5}$

Step 3.6

Cancel the common factor of $72$ and $5$ .

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Step 3.6.1

Rewrite $72$ as $1 (72)$ .

$x \geq \frac{1 (72)}{5}$

Step 3.6.2

Cancel the common factors.

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Step 3.6.2.1

Rewrite $5$ as $1 (5)$ .

$x \geq \frac{1 \cdot 72}{1 \cdot 5}$

Step 3.6.2.2

Cancel the common factor.

$x \geq \frac{1 \cdot 72}{1 \cdot 5}$

Step 3.6.2.3

Rewrite the expression.

$x \geq \frac{72}{5}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq \frac{72}{5}$

Interval Notation:

$[\frac{72}{5}, \infty)$