\(a. |x+2|+5x=4\) (a)
* Xét \(x+2 \ge0 \Leftrightarrow x \ge -2\)
\((a) \Leftrightarrow x+2+5x=4\)
\(\Leftrightarrow 6x=2\)
\(\Leftrightarrow x=\frac{1}{3}\) (thỏa mãn điều kiện}
* Xét \(x+2 <0 \Leftrightarrow x < -2\)
\((a)\Leftrightarrow -x-2+5x=4\)
\(\Leftrightarrow 4x=6\)
\(\Leftrightarrow x=\frac{3}{2}\) (không thỏa mãn điều kiện)
Vậy \(x=\frac{1}{3}\)
\(b. x-\frac{20}{11.13}-\frac{20}{13.15}-\frac{20}{15.17}-...-\frac{20}{53.55}=\frac{3}{11}\)
\(\Leftrightarrow x-10.(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{53.55})=\frac{3}{11}\)
\(\Leftrightarrow x-10.(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{53}-\frac{1}{55})=\frac{3}{11}\)
\(\Leftrightarrow x-10.(\frac{1}{11}-\frac{1}{55})=\frac{3}{11}\)
\(\Leftrightarrow x-\frac{8}{11}=\frac{3}{11}\)
\(\Leftrightarrow x=1\)
Vậy x=1
Chúc bạn học tốt!