Solve the Inequality for y -4(2y+3)<=20-4y

$- 4 (2 y + 3) \leq 20 - 4 y$

Simplify $- 4 (2 y + 3)$ .

Rewrite.

$0 + 0 - 4 (2 y + 3) \leq 20 - 4 y$

Simplify by adding zeros.

$- 4 (2 y + 3) \leq 20 - 4 y$

Apply the distributive property.

$- 4 (2 y) - 4 \cdot 3 \leq 20 - 4 y$

Multiply.

Multiply $2$ by $- 4$ .

$- 8 y - 4 \cdot 3 \leq 20 - 4 y$

Multiply $- 4$ by $3$ .

$- 8 y - 12 \leq 20 - 4 y$

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

Add $4 y$ to both sides of the inequality.

$- 8 y - 12 + 4 y \leq 20$

Add $- 8 y$ and $4 y$ .

$- 4 y - 12 \leq 20$

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

Add $12$ to both sides of the inequality.

$- 4 y \leq 20 + 12$

Add $20$ and $12$ .

$- 4 y \leq 32$

Divide each term in $- 4 y \leq 32$ by $- 4$ and simplify.

Divide each term in $- 4 y \leq 32$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 y}{- 4} \geq \frac{32}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} \geq \frac{32}{- 4}$

Divide $y$ by $1$ .

$y \geq \frac{32}{- 4}$

Simplify the right side.

Divide $32$ by $- 4$ .

$y \geq - 8$

The result can be shown in multiple forms.

Inequality Form:

$y \geq - 8$

Interval Notation:

$[- 8, \infty)$

Solve the Inequality for y -4(2y+3)<=20-4y

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