Solve the Inequality for y y-5(y+1)>=2y-5

$y - 5 (y + 1) \geq 2 y - 5$

Step 1

Simplify $y - 5 (y + 1)$ .

Simplify each term.

Apply the distributive property.

$y - 5 y - 5 \cdot 1 \geq 2 y - 5$

Multiply $- 5$ by $1$ .

$y - 5 y - 5 \geq 2 y - 5$

Subtract $5 y$ from $y$ .

$- 4 y - 5 \geq 2 y - 5$

Step 2

Move all terms containing $y$ to the left side of the inequality.

Subtract $2 y$ from both sides of the inequality.

$- 4 y - 5 - 2 y \geq - 5$

Subtract $2 y$ from $- 4 y$ .

$- 6 y - 5 \geq - 5$

Step 3

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

Add $5$ to both sides of the inequality.

$- 6 y \geq - 5 + 5$

Add $- 5$ and $5$ .

$- 6 y \geq 0$

Step 4

Divide each term in $- 6 y \geq 0$ by $- 6$ and simplify.

Divide each term in $- 6 y \geq 0$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 y}{- 6} \leq \frac{0}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} \leq \frac{0}{- 6}$

Divide $y$ by $1$ .

$y \leq \frac{0}{- 6}$

Simplify the right side.

Divide $0$ by $- 6$ .

$y \leq 0$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$y \leq 0$

Interval Notation:

$(- \infty, 0]$

Solve the Inequality for y y-5(y+1)>=2y-5

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