Final answer:
The solution to the compound inequality (16)/(8)<(y+3)/(4)<(25)/(8) is the interval (5, 9.5) in decimal form, which represents the values of 'y' that satisfy the inequality.
Step-by-step explanation:
To solve the compound inequality (16)/(8)<(y+3)/(4)<(25)/(8), we need to first simplify each part of the inequality and then solve for 'y'.
First, simplify the fractions: (16)/(8) simplifies to 2 and (25)/(8) remains as it is because it cannot be simplified further. So the inequality becomes: 2 < (y+3)/4 < 25/8.
Next, we'll multiply all parts of the inequality by 4 to get rid of the denominator:
- 4 * 2 < y + 3 < 4 * (25/8)
- 8 < y + 3 < 12.5
Subtracting 3 from all parts of the inequality gives us the solution for y:
- 8 - 3 < y < 12.5 - 3
- 5 < y < 9.5
The interval notation for this solution is (5, 9.5).