Solve the Inequality for y 4(y-3)<=4(2y+1)

$4 (y - 3) \leq 4 (2 y + 1)$

Step 1

Simplify $4 (y - 3)$ .

Rewrite.

$0 + 0 + 4 (y - 3) \leq 4 (2 y + 1)$

Simplify by adding zeros.

$4 (y - 3) \leq 4 (2 y + 1)$

Apply the distributive property.

$4 y + 4 \cdot - 3 \leq 4 (2 y + 1)$

Multiply $4$ by $- 3$ .

$4 y - 12 \leq 4 (2 y + 1)$

Step 2

Simplify $4 (2 y + 1)$ .

Apply the distributive property.

$4 y - 12 \leq 4 (2 y) + 4 \cdot 1$

Multiply.

Multiply $2$ by $4$ .

$4 y - 12 \leq 8 y + 4 \cdot 1$

Multiply $4$ by $1$ .

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

Step 3

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

Subtract $8 y$ from both sides of the inequality.

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

Subtract $8 y$ from $4 y$ .

$- 4 y - 12 \leq 4$

Step 4

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

Add $12$ to both sides of the inequality.

$- 4 y \leq 4 + 12$

Add $4$ and $12$ .

$- 4 y \leq 16$

Step 5

Divide each term in $- 4 y \leq 16$ by $- 4$ and simplify.

Divide each term in $- 4 y \leq 16$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 y}{- 4} \geq \frac{16}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} \geq \frac{16}{- 4}$

Divide $y$ by $1$ .

$y \geq \frac{16}{- 4}$

Simplify the right side.

Divide $16$ by $- 4$ .

$y \geq - 4$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$y \geq - 4$

Interval Notation:

$[- 4, \infty)$

Solve the Inequality for y 4(y-3)<=4(2y+1)

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