Question

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

Answer 1

To solve the inequality \( \sqrt{m} + 17 < 24 \), we can start by isolating \( \sqrt{m} \).

1. Subtract 17 from both sides of the inequality:

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

\[
\sqrt{m} < 7
\]

2. Next, we square both sides to eliminate the square root (remember that squaring both sides preserves the inequality since both sides are non-negative):

\[
m < 7^2
\]

\[
m < 49
\]

Thus, the values of \( m \) that satisfy the inequality \( \sqrt{m} + 17 < 24 \) are all values \( m < 49 \).

So any value of \( m \) that is less than 49 will make the inequality true.