Question

Which of the following values for m makes the inequality m−−√+17<24
true?(1 point)
Responses

49
49

48
48

50
50

64

Answer 1

To solve the inequality \( \sqrt{m} + 17 < 24 \), we can first isolate the square root term:

1. Subtract 17 from both sides:

\[
\sqrt{m} < 24 - 17
\]

\[
\sqrt{m} < 7
\]

2. Next, square both sides to eliminate the square root (note that \( \sqrt{m} \) is always non-negative):

\[
m < 7^2
\]

\[
m < 49
\]

Now we need to determine which provided value(s) for \( m \) makes the inequality true:

- 49: Not true since \( m < 49 \)
- 48: True since \( 48 < 49 \)
- 50: Not true since \( 50 > 49 \)
- 64: Not true since \( 64 > 49 \)

Thus, the only value that makes the inequality true is **48**.