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