Solve the Inequality for y -4<=4(6y-12)-2y

$- 4 \leq 4 (6 y - 12) - 2 y$

Rewrite so $y$ is on the left side of the inequality.

$4 (6 y - 12) - 2 y \geq - 4$

Simplify $4 (6 y - 12) - 2 y$ .

Simplify each term.

Apply the distributive property.

$4 (6 y) + 4 \cdot - 12 - 2 y \geq - 4$

Multiply $6$ by $4$ .

$24 y + 4 \cdot - 12 - 2 y \geq - 4$

Multiply $4$ by $- 12$ .

$24 y - 48 - 2 y \geq - 4$

Subtract $2 y$ from $24 y$ .

$22 y - 48 \geq - 4$

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

Add $48$ to both sides of the inequality.

$22 y \geq - 4 + 48$

Add $- 4$ and $48$ .

$22 y \geq 44$

Divide each term in $22 y \geq 44$ by $22$ and simplify.

Divide each term in $22 y \geq 44$ by $22$ .

$\frac{22 y}{22} \geq \frac{44}{22}$

Simplify the left side.

Cancel the common factor of $22$ .

Cancel the common factor.

$\frac{22 y}{22} \geq \frac{44}{22}$

Divide $y$ by $1$ .

$y \geq \frac{44}{22}$

Simplify the right side.

Divide $44$ by $22$ .

$y \geq 2$

The result can be shown in multiple forms.

Inequality Form:

$y \geq 2$

Interval Notation:

$[2, \infty)$