Question

Li’s brother used the work shown to determine that he must grow at most 6 inches to be able to ride the roller coaster.

48 less-than-or-equal-to h + 42. 48 minus 42 less-than-or-equal-to h + 42 minus 42. 6 less-than-or-equal-to h.

Is this correct? Explain.

Answer 1

The algebra is done correctly, but the conclusion is reversed.

Start with 48 ≤ h + 42 (final height must be at least 48). Subtract 42 from both sides: 6 ≤ h, which is the same as h ≥ 6. That means he must grow at least 6 inches (6 inches or more).

“At most 6 inches” would be h ≤ 6, which is the opposite of the inequality found. For example, if h = 5 then 42 + 5 = 47 (too short); if h = 6 then 42 + 6 = 48 (just enough); if h = 7 he is also tall enough.