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Answer :
Sure! Let's break down the problem step-by-step to find the correct inequality:
1. Understand the problem:
- Riders need to be at least 48 inches tall to go on the roller coaster.
- Li's little brother is 3 feet 6 inches tall.
- We need to create an inequality to show how many inches Li's brother must grow to meet the height requirement.
2. Convert Li's little brother's height to inches:
- Since [tex]\(12 \text{ inches} = 1 \text{ foot}\)[/tex], we can convert the height:
- [tex]\(3 \text{ feet} = 3 \times 12 = 36 \text{ inches}\)[/tex]
- Adding the additional 6 inches, we get:
- [tex]\(36 \text{ inches} + 6 \text{ inches} = 42 \text{ inches}\)[/tex]
3. Set up the inequality:
- We need to find how many more inches Li's brother must grow to reach the height requirement of 48 inches. Let [tex]\(x\)[/tex] represent the additional inches he needs to grow.
- Currently, he is 42 inches tall.
- To be able to ride, his total height (42 inches + [tex]\(x\)[/tex]) must be at least 48 inches. This can be represented by the inequality:
[tex]\[ 42 + x \geq 48 \][/tex]
4. Simplify the inequality:
- Subtract 42 from both sides to isolate [tex]\(x\)[/tex]:
[tex]\[ x \geq 48 - 42 \][/tex]
[tex]\[ x \geq 6 \][/tex]
Thus, he needs to grow at least 6 more inches. Now, we relate this back to the provided inequality options:
Looking deeper into the provided inequalities:
- [tex]\(48 \geq h - 42\)[/tex]
- [tex]\(48 \leq h - 42\)[/tex]
- [tex]\(48 \geq h + 42\)[/tex]
- [tex]\(48 \leq h + 42\)[/tex]
The appropriate inequality using the conversion and height becomes:
[tex]\[ 48 \leq h + 42 \][/tex]
This checks out against the setup of our problem and indicates the number of inches he must grow to be calculated properly.
Thus, the correct inequality is:
[tex]\[ 48 \leq h + 42 \][/tex]
1. Understand the problem:
- Riders need to be at least 48 inches tall to go on the roller coaster.
- Li's little brother is 3 feet 6 inches tall.
- We need to create an inequality to show how many inches Li's brother must grow to meet the height requirement.
2. Convert Li's little brother's height to inches:
- Since [tex]\(12 \text{ inches} = 1 \text{ foot}\)[/tex], we can convert the height:
- [tex]\(3 \text{ feet} = 3 \times 12 = 36 \text{ inches}\)[/tex]
- Adding the additional 6 inches, we get:
- [tex]\(36 \text{ inches} + 6 \text{ inches} = 42 \text{ inches}\)[/tex]
3. Set up the inequality:
- We need to find how many more inches Li's brother must grow to reach the height requirement of 48 inches. Let [tex]\(x\)[/tex] represent the additional inches he needs to grow.
- Currently, he is 42 inches tall.
- To be able to ride, his total height (42 inches + [tex]\(x\)[/tex]) must be at least 48 inches. This can be represented by the inequality:
[tex]\[ 42 + x \geq 48 \][/tex]
4. Simplify the inequality:
- Subtract 42 from both sides to isolate [tex]\(x\)[/tex]:
[tex]\[ x \geq 48 - 42 \][/tex]
[tex]\[ x \geq 6 \][/tex]
Thus, he needs to grow at least 6 more inches. Now, we relate this back to the provided inequality options:
Looking deeper into the provided inequalities:
- [tex]\(48 \geq h - 42\)[/tex]
- [tex]\(48 \leq h - 42\)[/tex]
- [tex]\(48 \geq h + 42\)[/tex]
- [tex]\(48 \leq h + 42\)[/tex]
The appropriate inequality using the conversion and height becomes:
[tex]\[ 48 \leq h + 42 \][/tex]
This checks out against the setup of our problem and indicates the number of inches he must grow to be calculated properly.
Thus, the correct inequality is:
[tex]\[ 48 \leq h + 42 \][/tex]
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