Which of the following values for m makes the inequality m−−√+17<24

Question

true?(1 point)
Responses

64
64

49
49

48
48

50

Answer 1

To solve the inequality \( \sqrt{m} + 17 < 24 \), we'll first isolate \( \sqrt{m} \):

1. Subtract 17 from both sides:

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

\[ \sqrt{m} < 7 \]

2. Now, square both sides to eliminate the square root (note this does not change the inequality since both sides are positive):

\[ m < 7^2 \]

\[ m < 49 \]

Now, from the options given, we need to find values of \( m \) that satisfy \( m < 49 \):

• 64: Does not satisfy \( m < 49 \)
• 49: Does not satisfy \( m < 49 \)
• 48: Satisfies \( m < 49 \)
• 50: Does not satisfy \( m < 49 \)

Therefore, the value for \( m \) that makes the inequality true is:

48