Algebra Examples

$- y + 5 \geq 9$ or $3 y + 4 < - 5$

Step 1

Simplify the first inequality.

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Step 1.1

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

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Step 1.1.1

Subtract $5$ from both sides of the inequality.

$- y \geq 9 - 5$ or $3 y + 4 < - 5$

Step 1.1.2

Subtract $5$ from $9$ .

$- y \geq 4$ or $3 y + 4 < - 5$

Step 1.2

Divide each term in $- y \geq 4$ by $- 1$ and simplify.

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Step 1.2.1

Divide each term in $- y \geq 4$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} \leq \frac{4}{- 1}$ or $3 y + 4 < - 5$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} \leq \frac{4}{- 1}$ or $3 y + 4 < - 5$

Step 1.2.2.2

Divide $y$ by $1$ .

$y \leq \frac{4}{- 1}$ or $3 y + 4 < - 5$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $4$ by $- 1$ .

$y \leq - 4$ or $3 y + 4 < - 5$

Step 2

Simplify the second inequality.

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Step 2.1

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

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Step 2.1.1

Subtract $4$ from both sides of the inequality.

$y \leq - 4$ or $3 y < - 5 - 4$

Step 2.1.2

Subtract $4$ from $- 5$ .

$y \leq - 4$ or $3 y < - 9$

Step 2.2

Divide each term in $3 y < - 9$ by $3$ and simplify.

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Step 2.2.1

Divide each term in $3 y < - 9$ by $3$ .

$y \leq - 4$ or $\frac{3 y}{3} < \frac{- 9}{3}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.1.1

Cancel the common factor.

$y \leq - 4$ or $\frac{3 y}{3} < \frac{- 9}{3}$

Step 2.2.2.1.2

Divide $y$ by $1$ .

$y \leq - 4$ or $y < \frac{- 9}{3}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $- 9$ by $3$ .

$y \leq - 4$ or $y < - 3$

Step 3

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

$y < - 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$y < - 3$

Interval Notation:

$(- \infty, - 3)$

Step 5