To determine which values satisfy the inequality [tex]\( 5 < y - 8 \)[/tex], we will go through the steps for each value provided.
The given inequality is:
[tex]\[ 5 < y - 8 \][/tex]
Let's begin solving the inequality step-by-step for each value:
1. When [tex]\( y = 8 \)[/tex]:
[tex]\[ 5 < 8 - 8 \][/tex]
[tex]\[ 5 < 0 \][/tex]
This is false, so [tex]\( y = 8 \)[/tex] does not satisfy the inequality.
2. When [tex]\( y = 9 \)[/tex]:
[tex]\[ 5 < 9 - 8 \][/tex]
[tex]\[ 5 < 1 \][/tex]
This is also false, so [tex]\( y = 9 \)[/tex] does not satisfy the inequality.
3. When [tex]\( y = 13 \)[/tex]:
[tex]\[ 5 < 13 - 8 \][/tex]
[tex]\[ 5 < 5 \][/tex]
This is false as well, so [tex]\( y = 13 \)[/tex] does not satisfy the inequality.
4. When [tex]\( y = 15 \)[/tex]:
[tex]\[ 5 < 15 - 8 \][/tex]
[tex]\[ 5 < 7 \][/tex]
This is true, so [tex]\( y = 15 \)[/tex] satisfies the inequality.
5. When [tex]\( y = 20 \)[/tex]:
[tex]\[ 5 < 20 - 8 \][/tex]
[tex]\[ 5 < 12 \][/tex]
This is also true, so [tex]\( y = 20 \)[/tex] satisfies the inequality.
Therefore, the values that satisfy the inequality [tex]\( 5 < y - 8 \)[/tex] are:
[tex]\[ y = 15 \][/tex]
[tex]\[ y = 20 \][/tex]
So the values that are solutions are 15 and 20.
