Solve |y + 2| > 6
{y|y < -6 or y > 6}
{y|y < -4 or y > 4}
{y|y < -8 or y > 4}
The correct solution is {y|y < -8 or y > 4}.
To solve the inequality |y + 2| > 6, we need to split it into two separate inequalities.
First, we solve for y + 2 > 6:
y + 2 > 6
Subtract 2 from both sides:
y > 6 - 2
y > 4
Second, we solve for -(y + 2) > 6:
-(y + 2) > 6
Multiply both sides by -1 (which flips the inequality sign):
y + 2 < -6
Subtract 2 from both sides:
y < -6 - 2
y < -8
Combining both inequalities, we get the solution:
y < -8 or y > 4
Therefore, the correct answer is:
{y|y < -8 or y > 4}.
To solve the inequality |y + 2| > 6, we can break it down into two cases: y + 2 > 6 and y + 2 < -6.
Case 1: y + 2 > 6
In this case, we isolate y:
y > 6 - 2
y > 4
Case 2: y + 2 < -6
Again, we isolate y:
y < -6 - 2
y < -8
Combining both cases, we have two sets of solutions:
{y | y > 4} and {y | y < -8}
Therefore, the correct answer is {y | y < -8 or y > 4}.