To determine the number of months \( x \) that Michael needs to wait until he is tall enough to ride, we need to set up an inequality based on his current height and his growth rate.
Michael is currently 42 inches tall and grows at a rate of \( 3/4 \) inch per month. After \( x \) months, his height will be:
\[ 42 + \frac{3}{4}x \]
We want this height to be at least 48 inches, which leads us to the inequality:
\[ 42 + \frac{3}{4}x \geq 48 \]
To isolate the term with \( x \), we can rearrange this inequality:
\[ \frac{3}{4}x \geq 48 - 42 \]
\[ \frac{3}{4}x \geq 6 \]
Now, if we look at the options you provided, the one that reflects the height Michael will reach after \( x \) months and ensure it is at least 48 inches tall is:
\[ \frac{3}{4}x + 42 \geq 48 \]
Thus, the correct inequality from your choices is:
3/4x + 42 ≥ 48
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