Solve the Inequality for y 3y+2>=5y+8

$3 y + 2 \geq 5 y + 8$

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

Subtract $5 y$ from both sides of the inequality.

$3 y + 2 - 5 y \geq 8$

Subtract $5 y$ from $3 y$ .

$- 2 y + 2 \geq 8$

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

Subtract $2$ from both sides of the inequality.

$- 2 y \geq 8 - 2$

Subtract $2$ from $8$ .

$- 2 y \geq 6$

Divide each term in $- 2 y \geq 6$ by $- 2$ and simplify.

Divide each term in $- 2 y \geq 6$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} \leq \frac{6}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} \leq \frac{6}{- 2}$

Divide $y$ by $1$ .

$y \leq \frac{6}{- 2}$

Simplify the right side.

Divide $6$ by $- 2$ .

$y \leq - 3$

The result can be shown in multiple forms.

Inequality Form:

$y \leq - 3$

Interval Notation:

$(- \infty, - 3]$

Solve the Inequality for y 3y+2>=5y+8

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