Question
(1) Consider the inequality \( t+9 \leq 12 \). (a) Make a list of 5 possible solutions for \( t \).
Ask by Dickson Fernandez. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Possible solutions for \( t \) are:
1. \( t = -5 \)
2. \( t = 0 \)
3. \( t = 2 \)
4. \( t = 3 \)
5. \( t = 1.5 \)
Solution
To solve the inequality \( t + 9 \leq 12 \), follow these steps:
1. **Isolate \( t \):**
\[
t + 9 \leq 12 \\
t \leq 12 - 9 \\
t \leq 3
\]
This means that any value of \( t \) that is **less than or equal to 3** satisfies the inequality.
### (a) Five Possible Solutions for \( t \):
Here are five different values for \( t \) that satisfy \( t \leq 3 \):
1. **\( t = -5 \)**
\[
-5 + 9 = 4 \leq 12 \quad \text{(True)}
\]
2. **\( t = 0 \)**
\[
0 + 9 = 9 \leq 12 \quad \text{(True)}
\]
3. **\( t = 2 \)**
\[
2 + 9 = 11 \leq 12 \quad \text{(True)}
\]
4. **\( t = 3 \)**
\[
3 + 9 = 12 \leq 12 \quad \text{(True)}
\]
5. **\( t = 1.5 \)**
\[
1.5 + 9 = 10.5 \leq 12 \quad \text{(True)}
\]
All these values of \( t \) satisfy the original inequality \( t + 9 \leq 12 \).
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The Deep Dive
To solve the inequality \( t + 9 \leq 12 \), we first subtract 9 from both sides, resulting in \( t \leq 3 \). Now, let’s find 5 possible solutions for \( t \): 1. \( t = 0 \) 2. \( t = 1 \) 3. \( t = 2 \) 4. \( t = 3 \) 5. \( t = -5 \) All these values satisfy the inequality, as they are less than or equal to 3!