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Answer :
To determine which situation can be modeled by the inequality [tex]\(3x + 5 \geq 12\)[/tex], let's break down the inequality and see which scenario fits.
First, let's simplify the inequality:
1. Start with the inequality: [tex]\(3x + 5 \geq 12\)[/tex].
2. Subtract 5 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\(3x \geq 7\)[/tex].
3. Divide both sides by 3 to solve for [tex]\(x\)[/tex]:
[tex]\(x \geq \frac{7}{3}\)[/tex].
This means that [tex]\(x\)[/tex] (the quantity we're interested in for the situation) must be at least 2.33 (approximately). Now, let's match this with the situations:
1. Ellie's car situation:
She uses 5 gallons to get to work, and the car holds at least 12 gallons. This doesn't seem to involve a step-wise increase (like adding a certain amount regularly).
2. April's writing situation:
April starts writing for 5 minutes and adds 3 minutes weekly to reach no more than 12 minutes. This situation is about decreasing to not exceed a certain limit, not about reaching at least a certain amount.
3. Ivy's biking situation:
Ivy starts biking 3 miles and adds 5 miles each month, aiming to bike at least 12 miles. This matches our inequality because she adds 5 miles monthly to meet or exceed the goal of 12 miles. We begin with 3 miles and need to reach at least 12 miles, which fits the structure of adding a set amount regularly.
4. Amir's notes situation:
Amir has written 5 notes and needs to complete at least 12 in total; the time frame for writing notes each day is 3 days. This situation focuses on distributing already known work (notes) and time rather than regularly accumulating towards a target.
The situation that best matches the inequality [tex]\(3x + 5 \geq 12\)[/tex] is Ivy's biking situation, where the monthly increase adds towards a minimum biking goal.
First, let's simplify the inequality:
1. Start with the inequality: [tex]\(3x + 5 \geq 12\)[/tex].
2. Subtract 5 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\(3x \geq 7\)[/tex].
3. Divide both sides by 3 to solve for [tex]\(x\)[/tex]:
[tex]\(x \geq \frac{7}{3}\)[/tex].
This means that [tex]\(x\)[/tex] (the quantity we're interested in for the situation) must be at least 2.33 (approximately). Now, let's match this with the situations:
1. Ellie's car situation:
She uses 5 gallons to get to work, and the car holds at least 12 gallons. This doesn't seem to involve a step-wise increase (like adding a certain amount regularly).
2. April's writing situation:
April starts writing for 5 minutes and adds 3 minutes weekly to reach no more than 12 minutes. This situation is about decreasing to not exceed a certain limit, not about reaching at least a certain amount.
3. Ivy's biking situation:
Ivy starts biking 3 miles and adds 5 miles each month, aiming to bike at least 12 miles. This matches our inequality because she adds 5 miles monthly to meet or exceed the goal of 12 miles. We begin with 3 miles and need to reach at least 12 miles, which fits the structure of adding a set amount regularly.
4. Amir's notes situation:
Amir has written 5 notes and needs to complete at least 12 in total; the time frame for writing notes each day is 3 days. This situation focuses on distributing already known work (notes) and time rather than regularly accumulating towards a target.
The situation that best matches the inequality [tex]\(3x + 5 \geq 12\)[/tex] is Ivy's biking situation, where the monthly increase adds towards a minimum biking goal.
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