Solve the Inequality for y 3/5(15y-5)>=5(2y+1)

$\frac{3}{5} (15 y - 5) \geq 5 (2 y + 1)$

Simplify $\frac{3}{5} \cdot (15 y - 5)$ .

Start simplifying.

$0 + 0 + \frac{3}{5} \cdot (15 y - 5) \geq 5 (2 y + 1)$

Simplify by adding zeros.

$\frac{3}{5} \cdot (15 y - 5) \geq 5 (2 y + 1)$

Apply the distributive property.

$\frac{3}{5} (15 y) + \frac{3}{5} \cdot - 5 \geq 5 (2 y + 1)$

Cancel the common factor of $5$ .

Factor $5$ out of $15 y$ .

$\frac{3}{5} (5 (3 y)) + \frac{3}{5} \cdot - 5 \geq 5 (2 y + 1)$

Cancel the common factor.

$\frac{3}{5} (5 (3 y)) + \frac{3}{5} \cdot - 5 \geq 5 (2 y + 1)$

Rewrite the expression.

$3 (3 y) + \frac{3}{5} \cdot - 5 \geq 5 (2 y + 1)$

Multiply $3$ by $3$ .

$9 y + \frac{3}{5} \cdot - 5 \geq 5 (2 y + 1)$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

$9 y + \frac{3}{5} \cdot (5 (- 1)) \geq 5 (2 y + 1)$

Cancel the common factor.

$9 y + \frac{3}{5} \cdot (5 \cdot - 1) \geq 5 (2 y + 1)$

Rewrite the expression.

$9 y + 3 \cdot - 1 \geq 5 (2 y + 1)$

Multiply $3$ by $- 1$ .

$9 y - 3 \geq 5 (2 y + 1)$

Simplify $5 (2 y + 1)$ .

Apply the distributive property.

$9 y - 3 \geq 5 (2 y) + 5 \cdot 1$

Multiply.

Multiply $2$ by $5$ .

$9 y - 3 \geq 10 y + 5 \cdot 1$

Multiply $5$ by $1$ .

$9 y - 3 \geq 10 y + 5$

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

Subtract $10 y$ from both sides of the inequality.

$9 y - 3 - 10 y \geq 5$

Subtract $10 y$ from $9 y$ .

$- y - 3 \geq 5$

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

Add $3$ to both sides of the inequality.

$- y \geq 5 + 3$

Add $5$ and $3$ .

$- y \geq 8$

Divide each term in $- y \geq 8$ by $- 1$ and simplify.

Divide each term in $- y \geq 8$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} \leq \frac{8}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} \leq \frac{8}{- 1}$

Divide $y$ by $1$ .

$y \leq \frac{8}{- 1}$

Simplify the right side.

Divide $8$ by $- 1$ .

$y \leq - 8$

The result can be shown in multiple forms.

Inequality Form:

$y \leq - 8$

Interval Notation:

$(- \infty, - 8]$

Solve the Inequality for y 3/5(15y-5)>=5(2y+1)

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