Sure! Let's solve the inequality [tex]\( 2 \geq \frac{y}{5} - 1 \)[/tex] step-by-step for the given [tex]\( y \)[/tex]-values: 15, 20, and 25.
### Step 1: Starting with the inequality
[tex]\[ 2 \geq \frac{y}{5} - 1 \][/tex]
### Step 2: Isolate [tex]\( \frac{y}{5} \)[/tex]
Add 1 to both sides of the inequality to move the constant term to the left side:
[tex]\[ 2 + 1 \geq \frac{y}{5} \][/tex]
This simplifies to:
[tex]\[ 3 \geq \frac{y}{5} \][/tex]
### Step 3: Clear the fraction by multiplying both sides by 5
[tex]\[ 3 \times 5 \geq y \][/tex]
[tex]\[ 15 \geq y \][/tex]
This tells us that [tex]\( y \)[/tex] must be less than or equal to 15.
### Step 4: Check each of the given [tex]\( y \)[/tex] values
- For [tex]\( y = 15 \)[/tex]:
[tex]\[ 15 \leq 15 \][/tex]
This is true.
- For [tex]\( y = 20 \)[/tex]:
[tex]\[ 20 \leq 15 \][/tex]
This is false.
- For [tex]\( y = 25 \)[/tex]:
[tex]\[ 25 \leq 15 \][/tex]
This is false.
### Conclusion
The only value that satisfies the inequality [tex]\( 2 \geq \frac{y}{5} - 1 \)[/tex] is [tex]\( y = 15 \)[/tex].
Therefore, the correct answer is:
A [tex]\( y = 15 \)[/tex]
