Question

Chứng minh:

a. Nếu \(a > 5\) thì \(\frac{{a - 1}}{2} - 2 > 0\).

b. Nếu \(b > 7\) thì \(4 - \frac{{b + 3}}{5} < 2\).

Answer 1

a. Ta có:

\(\begin{array}{l}\frac{{a - 1}}{2} - 2 > 0\\\frac{{a - 1}}{2} - \frac{4}{2} > 0\\\frac{{a - 5}}{2} > 0\\a - 5 > 0\\a > 5\end{array}\)

Vậy nếu \(a > 5\) thì \(\frac{{a - 1}}{2} - 2 > 0\).

b. Ta có:

\(\begin{array}{l}4 - \frac{{b + 3}}{5} < 2\\\frac{{20}}{5} - \frac{{b + 3}}{5} < \frac{{10}}{5}\\\frac{{20 - b - 3 - 10}}{5} < 0\\ - b + 7 < 0\\ - b <  - 7\\b > 7\end{array}\)

Vậy nếu \(b > 7\) thì \(4 - \frac{{b + 3}}{5} < 2\).