Solve |y - 2|<10
{y|-8 < y < 12}
{y|-8 < y < 8}
{y|-12 < y < 8}
The correct solution is {y|-8 < y < 12}.
To solve the inequality |y - 2| < 10, we can approach it by breaking it into two separate cases:
Case 1: (y - 2) < 10
In this case, you can remove the absolute value signs and solve for y:
y - 2 < 10
Add 2 to both sides of the inequality to isolate y:
y < 12
Case 2: -(y - 2) < 10
In this case, you need to remove the negative sign first by multiplying both sides of the inequality by -1:
y - 2 > -10
Add 2 to both sides of the inequality to isolate y:
y > -8
Therefore, combining the two cases, the solution to the inequality |y - 2| < 10 is:
-8 < y < 12.
So, the correct solution is {y|-8 < y < 12}.
To solve the inequality |y - 2| < 10, we need to consider two cases based on the absolute value.
Case 1: (y - 2) < 0
When (y - 2) < 0, the absolute value |y - 2| becomes -(y - 2). In this case, the inequality can be rewritten as -(y - 2) < 10.
To solve this inequality, we can multiply both sides by -1, but that also reverses the inequality sign:
(y - 2) > -10
Now, we can solve for y by adding 2 to both sides:
y > -10 + 2
y > -8
So, the first part of the solution is y > -8.
Case 2: (y - 2) >= 0
When (y - 2) >= 0, the absolute value |y - 2| remains (y - 2) unchanged. In this case, the inequality can be rewritten as (y - 2) < 10.
To solve this inequality, we can solve for y by adding 2 to both sides:
y < 10 + 2
y < 12
So, the second part of the solution is y < 12.
Combining the two cases, we have the solution:
-8 < y < 12
Therefore, the correct answer is {y| -8 < y < 12}.