Algebra Examples

$\frac{(4 - y)}{5} - 5 y \geq 0$

Step 1

Simplify $\frac{4 - y}{5} - 5 y$ .

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Step 1.1

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

$\frac{4 - y}{5} - 5 y \cdot \frac{5}{5} \geq 0$

Step 1.2

Simplify terms.

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Step 1.2.1

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

$\frac{4 - y}{5} + \frac{- 5 y \cdot 5}{5} \geq 0$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{4 - y - 5 y \cdot 5}{5} \geq 0$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Multiply $5$ by $- 5$ .

$\frac{4 - y - 25 y}{5} \geq 0$

Step 1.3.2

Subtract $25 y$ from $- y$ .

$\frac{4 - 26 y}{5} \geq 0$

Step 1.3.3

Factor $2$ out of $4 - 26 y$ .

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Step 1.3.3.1

Factor $2$ out of $4$ .

$\frac{2 (2) - 26 y}{5} \geq 0$

Step 1.3.3.2

Factor $2$ out of $- 26 y$ .

$\frac{2 (2) + 2 (- 13 y)}{5} \geq 0$

Step 1.3.3.3

Factor $2$ out of $2 (2) + 2 (- 13 y)$ .

$\frac{2 (2 - 13 y)}{5} \geq 0$

Step 2

Multiply both sides by $5$ .

$\frac{2 (2 - 13 y)}{5} \cdot 5 \geq 0 \cdot 5$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{2 (2 - 13 y)}{5} \cdot 5$ .

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Step 3.1.1.1

Cancel the common factor of $5$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{2 (2 - 13 y)}{5} \cdot 5 \geq 0 \cdot 5$

Step 3.1.1.1.2

Rewrite the expression.

$2 (2 - 13 y) \geq 0 \cdot 5$

Step 3.1.1.2

Apply the distributive property.

$2 \cdot 2 + 2 (- 13 y) \geq 0 \cdot 5$

Step 3.1.1.3

Simplify the expression.

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Step 3.1.1.3.1

Multiply $2$ by $2$ .

$4 + 2 (- 13 y) \geq 0 \cdot 5$

Step 3.1.1.3.2

Multiply $- 13$ by $2$ .

$4 - 26 y \geq 0 \cdot 5$

Step 3.1.1.3.3

Reorder $4$ and $- 26 y$ .

$- 26 y + 4 \geq 0 \cdot 5$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $0$ by $5$ .

$- 26 y + 4 \geq 0$

Step 4

Solve for $y$ .

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Step 4.1

Subtract $4$ from both sides of the inequality.

$- 26 y \geq - 4$

Step 4.2

Divide each term in $- 26 y \geq - 4$ by $- 26$ and simplify.

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Step 4.2.1

Divide each term in $- 26 y \geq - 4$ by $- 26$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 26 y}{- 26} \leq \frac{- 4}{- 26}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $- 26$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{- 26 y}{- 26} \leq \frac{- 4}{- 26}$

Step 4.2.2.1.2

Divide $y$ by $1$ .

$y \leq \frac{- 4}{- 26}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Cancel the common factor of $- 4$ and $- 26$ .

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Step 4.2.3.1.1

Factor $- 2$ out of $- 4$ .

$y \leq \frac{- 2 (2)}{- 26}$

Step 4.2.3.1.2

Cancel the common factors.

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Step 4.2.3.1.2.1

Factor $- 2$ out of $- 26$ .

$y \leq \frac{- 2 \cdot 2}{- 2 \cdot 13}$

Step 4.2.3.1.2.2

Cancel the common factor.

$y \leq \frac{- 2 \cdot 2}{- 2 \cdot 13}$

Step 4.2.3.1.2.3

Rewrite the expression.

$y \leq \frac{2}{13}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$y \leq \frac{2}{13}$

Interval Notation:

$(- \infty, \frac{2}{13}]$