Algebra Examples

$30 < 5 (8 - y)$

Step 1

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

$5 (8 - y) > 30$

Step 2

Divide each term in $5 (8 - y) > 30$ by $5$ and simplify.

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Step 2.1

Divide each term in $5 (8 - y) > 30$ by $5$ .

$\frac{5 (8 - y)}{5} > \frac{30}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5 (8 - y)}{5} > \frac{30}{5}$

Step 2.2.1.2

Divide $8 - y$ by $1$ .

$8 - y > \frac{30}{5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $30$ by $5$ .

$8 - y > 6$

Step 3

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

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Step 3.1

Subtract $8$ from both sides of the inequality.

$- y > 6 - 8$

Step 3.2

Subtract $8$ from $6$ .

$- y > - 2$

Step 4

Divide each term in $- y > - 2$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- y > - 2$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} < \frac{- 2}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} < \frac{- 2}{- 1}$

Step 4.2.2

Divide $y$ by $1$ .

$y < \frac{- 2}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 2$ by $- 1$ .

$y < 2$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$y < 2$

Interval Notation:

$(- \infty, 2)$