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### Given Information:
- Shane and Abha collected a total of no less than 2000 cans.
- Abha collected 178 more cans than Shane.
  
Let \( S \) represent the number of cans Shane collected. Then Abha collected \( S + 178 \) cans.

### The total number of cans they collected is:

\[
S + (S + 178) = 2S + 178
\]

### The total number of cans must be no less than 2000, so we can set up the inequality:

\[
2S + 178 \geq 2000
\]

### To solve the inequality:
1. Subtract 178 from both sides:

\[
2S \geq 2000 - 178
\]
\[
2S \geq 1822
\]

2. Divide both sides by 2:

\[
S \geq \frac{1822}{2}
\]
\[
S \geq 911
\]

### Final Solution:
Shane must have collected **at least 911 cans**, so the solution set is \( S \geq 911 \).

Do you want more details or have any questions?  
Here are 5 related questions to expand your understanding:

1. How many cans did Abha collect if Shane collected exactly 911 cans?
2. What would the inequality be if Abha collected 200 more cans than Shane?
3. Can you verify the solution by plugging in \( S = 911 \) into the inequality?
4. How would the inequality change if the team collected no less than 2500 cans?
5. What if Abha collected 178 fewer cans than Shane? How would that affect the inequality?

**Tip:** Always check the boundary value when solving inequalities, especially when working with "no less than" or "no more than" phrases.

Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling. Abha collected 178 more cans than Shane. Write an inequality to determine the number of cans, S, that Shane could have collected.

Learn how to solve the linear inequality 2S + 178 >= 2000 to determine how many cans Shane could have collected. This problem covers key algebraic concepts and the method for solving inequalities. Suitable for students in Grades 6-8.

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