To find the range of possible values for [tex]\( y \)[/tex] in the given inequality, we need to solve the compound inequality step-by-step. Initially, the inequality is:
[tex]\[ 19 < 30° + (2y - 9) < 21 \][/tex]
This can be simplified by treating 30° as a constant value. Let’s reframe our inequality:
[tex]\[ 19 < 30 + (2y - 9) < 21 \][/tex]
First, simplify the expression inside the inequality:
[tex]\[ 30 + (2y - 9) = 30 - 9 + 2y = 21 + 2y \][/tex]
Now, the inequality is:
[tex]\[ 19 < 21 + 2y < 21 \][/tex]
We can separate this compound inequality into two parts and solve each part separately.
First part:
[tex]\[ 19 < 21 + 2y \][/tex]
Subtract 21 from both sides of the inequality to isolate the term involving [tex]\( y \)[/tex]:
[tex]\[ 19 - 21 < 2y \][/tex]
[tex]\[ -2 < 2y \][/tex]
Divide both sides by 2:
[tex]\[ -1 < y \][/tex]
Second part:
[tex]\[ 21 + 2y < 21 \][/tex]
Subtract 21 from both sides of the inequality to isolate the term involving [tex]\( y \)[/tex]:
[tex]\[ 21 + 2y - 21 < 21 - 21 \][/tex]
[tex]\[ 2y < 0 \][/tex]
Divide both sides by 2:
[tex]\[ y < 0 \][/tex]
Combining the two parts, we get:
[tex]\[ -1 < y < 0 \][/tex]
Therefore, the range of possible values for [tex]\( y \)[/tex] is:
[tex]\[ -1 < y < 0 \][/tex]
Thus, the final answer is:
[tex]\[ -1 < y < 0 \][/tex]
