Let's solve the inequalities step by step:
### First Inequality
[tex]\[ y + (-6) \geq -13 \][/tex]
1. Simplify the expression inside the parentheses:
[tex]\[ y - 6 \geq -13 \][/tex]
2. To isolate [tex]\( y \)[/tex], add 6 to both sides of the inequality:
[tex]\[ y - 6 + 6 \geq -13 + 6 \][/tex]
3. Simplify:
[tex]\[ y \geq -7 \][/tex]
So the solution to the first inequality is:
[tex]\[ y \geq -7 \][/tex]
### Second Inequality
[tex]\[ -3y + 8 > -7 \][/tex]
1. To isolate the term with [tex]\( y \)[/tex], first subtract 8 from both sides of the inequality:
[tex]\[ -3y + 8 - 8 > -7 - 8 \][/tex]
2. Simplify:
[tex]\[ -3y > -15 \][/tex]
3. To solve for [tex]\( y \)[/tex], divide both sides by -3. Note that dividing by a negative number reverses the inequality sign:
[tex]\[ y < 5 \][/tex]
So the solution to the second inequality is:
[tex]\[ y < 5 \][/tex]
### Combined Solution
Since we are dealing with an "or" condition between the two inequalities, the solution is any [tex]\( y \)[/tex] that satisfies either of the inequalities:
[tex]\[ y \geq -7 \quad \text{or} \quad y < 5 \][/tex]
Thus, combining these, the complete solution is:
[tex]\[ -7 \leq y < 5 \][/tex]
The interval notation for this solution is:
[tex]\[ (-7, 5) \][/tex]
