Question

Tim x:
a,(x-3)(x+4)>0
b,|5/7. x-4| < 2/7

Answer 1

a) Ta có: \(\left(x-3\right)\left(x+4\right)>0\)

Nếu: \(\hept{\begin{cases}x-3>0\\x+4>0\end{cases}}\Leftrightarrow\hept{\begin{cases}x>3\\x>-4\end{cases}}\Rightarrow x>3\)

Nếu: \(\hept{\begin{cases}x-3< 0\\x+4< 0\end{cases}}\Leftrightarrow\hept{\begin{cases}x< 3\\x< -4\end{cases}}\Rightarrow x< -4\)

Vậy \(\orbr{\begin{cases}x>3\\x< -4\end{cases}}\)

Answer 2

b) Ta có: \(\left|\frac{5}{7}x-4\right|< \frac{2}{7}\)

\(\Leftrightarrow-\frac{2}{7}< \frac{5}{7}x-4< \frac{2}{7}\)

\(\Leftrightarrow\frac{26}{7}< \frac{5}{4}x< \frac{30}{7}\)

\(\Leftrightarrow\frac{104}{35}< x< \frac{24}{7}\)