Use the equation from part ​a) to set up an inequality. Solve the inequality to find the number of years after 2015 in which the percentage will occur. Then use that value to find the year. The equation is s=-2.0t+33.6 We need to find which year the percentage of smokers will fall below 4%

The given equation is:

\[
s = -2.0t + 33.6
\]

where:
- \( s \) is the percentage of smokers,
- \( t \) is the number of years after 2015.

We need to find the year when the percentage of smokers falls below 4%. This sets up the following inequality:

\[
-2.0t + 33.6 < 4
\]

### Steps to solve the inequality:

1. Subtract 33.6 from both sides:

\[
-2.0t < 4 - 33.6
\]

\[
-2.0t < -29.6
\]

2. Divide both sides by -2.0 (remember, dividing by a negative number reverses the inequality sign):

\[
t > \frac{-29.6}{-2.0}
\]

\[
t > 14.8
\]

### Interpretation:
The value \( t = 14.8 \) means that the percentage of smokers will fall below 4% after 14.8 years from 2015.

### Finding the year:
Add 14.8 years to 2015:

\[
2015 + 14.8 = 2029.8
\]

Thus, the percentage of smokers will fall below 4% sometime during the year **2030**.

Would you like further clarification on any part of the process?

Here are 5 relative questions:
1. How does dividing by a negative number affect inequalities?
2. Can you interpret what the slope of -2.0 in the equation represents?
3. Why is it important to reverse the inequality sign when dividing by a negative number?
4. How would the answer change if the threshold was 5% instead of 4%?
5. What does the constant 33.6 in the equation represent?

**Tip**: Always check the direction of inequalities when solving for variables, especially when multiplying or dividing by negative numbers!

Use the equation from part ​a) to set up an inequality. Solve the inequality to find the number of years after 2015 in which the percentage will occur. Then use that value to find the year. The equation is s=-2.0t+33.6. We need to find which year the percentage of smokers will fall below 4%.

Learn how to solve the linear inequality -2.0t + 33.6 < 4 to determine when the percentage of smokers will fall below 4%. This problem covers key algebraic concepts, such as solving inequalities and interpreting the solution. Suitable for students in Grades 8-10.

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