Algebra Examples

$9 \frac{4}{5} + y > - \frac{1}{5}$

Step 1

Simplify the left side.

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Step 1.1

Convert $9 \frac{4}{5}$ to an improper fraction.

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Step 1.1.1

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

$9 + \frac{4}{5} + y > - \frac{1}{5}$

Step 1.1.2

Add $9$ and $\frac{4}{5}$ .

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Step 1.1.2.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$9 \cdot \frac{5}{5} + \frac{4}{5} + y > - \frac{1}{5}$

Step 1.1.2.2

Combine $9$ and $\frac{5}{5}$ .

$\frac{9 \cdot 5}{5} + \frac{4}{5} + y > - \frac{1}{5}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{9 \cdot 5 + 4}{5} + y > - \frac{1}{5}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $9$ by $5$ .

$\frac{45 + 4}{5} + y > - \frac{1}{5}$

Step 1.1.2.4.2

Add $45$ and $4$ .

$\frac{49}{5} + y > - \frac{1}{5}$

Step 2

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

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Step 2.1

Subtract $\frac{49}{5}$ from both sides of the inequality.

$y > - \frac{1}{5} - \frac{49}{5}$

Step 2.2

Combine the numerators over the common denominator.

$y > \frac{- 1 - 49}{5}$

Step 2.3

Subtract $49$ from $- 1$ .

$y > \frac{- 50}{5}$

Step 2.4

Divide $- 50$ by $5$ .

$y > - 10$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$y > - 10$

Interval Notation:

$(- 10, \infty)$