Question
Which situation can be represented by the inequality 3x + 12 < 5x + 8
?
?
Answers
GPT-4o mini
To interpret the inequality \(3x + 12 < 5x + 8\), we can rewrite it in a more meaningful context.
1. **Setting the Scene**: Let’s assume you're comparing the total cost of two different options for a monthly subscription service. The costs could involve a base fee plus additional fees based on usage (which is represented by \(x\)).
2. **Breaking Down the Inequality**:
- The left side of the inequality \(3x + 12\) could represent the cost of Option A where you have a fixed fee of $12 and an additional variable cost based on usage, represented by \(3x\) (for example, $3 per hour of usage).
- The right side \(5x + 8\) represents the cost of Option B where you have a fixed fee of $8 and a higher variable cost of $5 per hour of usage.
3. **Interpreting the Inequality**:
The inequality \(3x + 12 < 5x + 8\) states that the total cost of Option A is less than the total cost of Option B.
4. **Finding the Value of \(x\)**:
If we solve the inequality to find out when Option A is cheaper than Option B:
\[
3x + 12 < 5x + 8
\]
Subtract \(3x\) from both sides:
\[
12 < 2x + 8
\]
Subtract 8 from both sides:
\[
4 < 2x
\]
Divide by 2:
\[
2 < x
\]
Thus, Option A will be cheaper than Option B when \(x\) (the usage) is greater than 2 hours.
**Conclusion**: The inequality \(3x + 12 < 5x + 8\) can represent a situation where you're deciding between two subscription services based on usage, with Option A being cheaper when your usage is more than 2 hours.
1. **Setting the Scene**: Let’s assume you're comparing the total cost of two different options for a monthly subscription service. The costs could involve a base fee plus additional fees based on usage (which is represented by \(x\)).
2. **Breaking Down the Inequality**:
- The left side of the inequality \(3x + 12\) could represent the cost of Option A where you have a fixed fee of $12 and an additional variable cost based on usage, represented by \(3x\) (for example, $3 per hour of usage).
- The right side \(5x + 8\) represents the cost of Option B where you have a fixed fee of $8 and a higher variable cost of $5 per hour of usage.
3. **Interpreting the Inequality**:
The inequality \(3x + 12 < 5x + 8\) states that the total cost of Option A is less than the total cost of Option B.
4. **Finding the Value of \(x\)**:
If we solve the inequality to find out when Option A is cheaper than Option B:
\[
3x + 12 < 5x + 8
\]
Subtract \(3x\) from both sides:
\[
12 < 2x + 8
\]
Subtract 8 from both sides:
\[
4 < 2x
\]
Divide by 2:
\[
2 < x
\]
Thus, Option A will be cheaper than Option B when \(x\) (the usage) is greater than 2 hours.
**Conclusion**: The inequality \(3x + 12 < 5x + 8\) can represent a situation where you're deciding between two subscription services based on usage, with Option A being cheaper when your usage is more than 2 hours.