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kudzordzifrancis

ANSWER

{y|y < -8 or y > 4}

EXPLANATION

The given absolute value equation is

[tex] |y + 2| \: > \: 6[/tex]

This implies that:

[tex](y + 2) \: > \: 6 \: or \: - (y + 2) \: > \: 6[/tex]

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

[tex]y + 2 \: > \: 6 \: or \: y + 2\: < \: - 6[/tex]

[tex]y \: > \: 6 - 2\: or \: y \: < \: - 6 - 2[/tex]

We simplify to get:

[tex]y \: > \: 4\: or \: y \: < \: - 8[/tex]

The correct answer is A.

gmany

Answer:

[tex]\large\boxed{\{y\ |\ y<-8\ or\ y>4\}}[/tex]

Step-by-step explanation:

[tex]|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\ |\ y<-8\ or\ y>4\}[/tex]

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