Y + 6 > -1 or y - 2 /leq 4

Answer 1

To solve the compound inequality \( Y + 6 > -1 \) or \( Y - 2 \leq 4 \), we'll solve each part separately.

First Inequality: \( Y + 6 > -1 \)

1. Subtract 6 from both sides: \[ Y > -1 - 6 \] \[ Y > -7 \]

Second Inequality: \( Y - 2 \leq 4 \)

1. Add 2 to both sides: \[ Y \leq 4 + 2 \] \[ Y \leq 6 \]

Combine the Results

Now we can combine the results from both inequalities:

1. \( Y > -7 \)
2. \( Y \leq 6 \)

Final Solution

The complete solution is: \[ -7 < Y \leq 6 \] This means \( Y \) can take any value greater than -7 and up to and including 6.