Solve the Inequality for y -2(7+y)>=-8(y+1)

$- 2 (7 + y) \geq - 8 (y + 1)$

Step 1

Simplify $- 2 (7 + y)$ .

Rewrite.

$0 + 0 - 2 (7 + y) \geq - 8 (y + 1)$

Simplify by adding zeros.

$- 2 (7 + y) \geq - 8 (y + 1)$

Apply the distributive property.

$- 2 \cdot 7 - 2 y \geq - 8 (y + 1)$

Multiply $- 2$ by $7$ .

$- 14 - 2 y \geq - 8 (y + 1)$

Step 2

Simplify $- 8 (y + 1)$ .

Apply the distributive property.

$- 14 - 2 y \geq - 8 y - 8 \cdot 1$

Multiply $- 8$ by $1$ .

$- 14 - 2 y \geq - 8 y - 8$

Step 3

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

Add $8 y$ to both sides of the inequality.

$- 14 - 2 y + 8 y \geq - 8$

Add $- 2 y$ and $8 y$ .

$- 14 + 6 y \geq - 8$

Step 4

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

Add $14$ to both sides of the inequality.

$6 y \geq - 8 + 14$

Add $- 8$ and $14$ .

$6 y \geq 6$

Step 5

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

Divide each term in $6 y \geq 6$ by $6$ .

$\frac{6 y}{6} \geq \frac{6}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} \geq \frac{6}{6}$

Divide $y$ by $1$ .

$y \geq \frac{6}{6}$

Simplify the right side.

Divide $6$ by $6$ .

$y \geq 1$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$y \geq 1$

Interval Notation:

$[1, \infty)$

Solve the Inequality for y -2(7+y)>=-8(y+1)

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