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Answer :
First, convert Li's little brother's height from feet and inches to inches. Since there are 12 inches in 1 foot, his height is
[tex]$$
3 \text{ feet } 6 \text{ inches } = 3 \times 12 + 6 = 36 + 6 = 42 \text{ inches}.
$$[/tex]
The roller coaster requires riders to be at least 48 inches tall. If we let [tex]$h$[/tex] be the number of inches he must grow, then his new height will be
[tex]$$
42 + h.
$$[/tex]
To be tall enough to ride, his new height must be at least 48 inches, giving the inequality
[tex]$$
42 + h \geq 48.
$$[/tex]
Rearranging this inequality, we obtain
[tex]$$
h \geq 48 - 42 \quad \Longrightarrow \quad h \geq 6.
$$[/tex]
This inequality indicates that he must grow at least 6 inches. To express the condition using the structure given in the multiple-choice options, note that the inequality
[tex]$$
42 + h \geq 48
$$[/tex]
can be rewritten as
[tex]$$
48 \leq h + 42.
$$[/tex]
Thus, the inequality that can be used to find how many inches he must grow is
[tex]$$
48 \leq h+42.
$$[/tex]
This corresponds to the fourth option provided.
[tex]$$
3 \text{ feet } 6 \text{ inches } = 3 \times 12 + 6 = 36 + 6 = 42 \text{ inches}.
$$[/tex]
The roller coaster requires riders to be at least 48 inches tall. If we let [tex]$h$[/tex] be the number of inches he must grow, then his new height will be
[tex]$$
42 + h.
$$[/tex]
To be tall enough to ride, his new height must be at least 48 inches, giving the inequality
[tex]$$
42 + h \geq 48.
$$[/tex]
Rearranging this inequality, we obtain
[tex]$$
h \geq 48 - 42 \quad \Longrightarrow \quad h \geq 6.
$$[/tex]
This inequality indicates that he must grow at least 6 inches. To express the condition using the structure given in the multiple-choice options, note that the inequality
[tex]$$
42 + h \geq 48
$$[/tex]
can be rewritten as
[tex]$$
48 \leq h + 42.
$$[/tex]
Thus, the inequality that can be used to find how many inches he must grow is
[tex]$$
48 \leq h+42.
$$[/tex]
This corresponds to the fourth option provided.
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