Question

Solve |y + 2| > 6

y < -8 or y > 4
y < -6 or y > 6
y < -4 or y > 4

Answer 1

`\large\boxed{\y\ }`

Explanation:

`|y+2|>6\iff y+2>6\ or\ y+2<-6\qquad\text{subtract 2 from both sides}\\\\y+2-2>6-2\ or\ y+2-2<-6-2\\\\y>4\ or\ y<-8\Rightarrow\y\`

Answer 2

y

EXPLANATION

The given absolute value equation is

`|y + 2| \: > \: 6`

This implies that:

`(y + 2) \: > \: 6 \: or \: - (y + 2) \: > \: 6`

Multiply through by -1 in the second inequality and reverse the sign.

`y + 2 \: > \: 6 \: or \: y + 2\: < \: - 6`

`y \: > \: 6 - 2\: or \: y \: < \: - 6 - 2`

We simplify to get:

`y \: > \: 4\: or \: y \: < \: - 8`

The correct answer is A.