Work out the largest integer value that \( n \) could take if \[ \frac{n}{5}+2<9 \]
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To solve the inequality \(\frac{n}{5}+2<9\), we first isolate \(\frac{n}{5}\): \[ \frac{n}{5} < 9 - 2 \] This simplifies to: \[ \frac{n}{5} < 7 \] Next, we multiply both sides by 5 to eliminate the fraction: \[ n < 35 \] Since we're looking for the largest integer value that \( n \) could take, we find that the largest integer less than 35 is: \[ n = 34 \] Thus, the largest integer value \( n \) could take is 34.
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