Solve the Inequality for y 5y^2-5y(y+4)>=100

$5 y^{2} - 5 y (y + 4) \geq 100$

Simplify $5 y^{2} - 5 y (y + 4)$ .

Simplify each term.

Apply the distributive property.

$5 y^{2} - 5 y \cdot y - 5 y \cdot 4 \geq 100$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$5 y^{2} - 5 (y \cdot y) - 5 y \cdot 4 \geq 100$

Multiply $y$ by $y$ .

$5 y^{2} - 5 y^{2} - 5 y \cdot 4 \geq 100$

Multiply $4$ by $- 5$ .

$5 y^{2} - 5 y^{2} - 20 y \geq 100$

Simplify by adding terms.

Subtract $5 y^{2}$ from $5 y^{2}$ .

$0 - 20 y \geq 100$

Subtract $20 y$ from $0$ .

$- 20 y \geq 100$

Divide each term in $- 20 y \geq 100$ by $- 20$ and simplify.

Divide each term in $- 20 y \geq 100$ by $- 20$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 20 y}{- 20} \leq \frac{100}{- 20}$

Simplify the left side.

Cancel the common factor of $- 20$ .

Cancel the common factor.

$\frac{- 20 y}{- 20} \leq \frac{100}{- 20}$

Divide $y$ by $1$ .

$y \leq \frac{100}{- 20}$

Simplify the right side.

Divide $100$ by $- 20$ .

$y \leq - 5$

The result can be shown in multiple forms.

Inequality Form:

$y \leq - 5$

Interval Notation:

$(- \infty, - 5]$

Solve the Inequality for y 5y^2-5y(y+4)>=100

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