a) \((4x+5):3-121:11=4\)
\((4x+5):3-11=4\)
\((4x+5):3=4+11\)
\((4x+5):3=15\)
\((4x+5)=15\times3\)
\(4x+5=45\)
\(4x=45-5\)
\(4x=40\)
\(x=40:4\)
\(x=4\)
a') \((4x+5):3-\dfrac{122}{11}=4\)
\((4x+5):3=4+\dfrac{122}{11}\)
\((4x+5):3=\dfrac{44}{11}+\dfrac{122}{11}\)
\((4x+5):3=\dfrac{44+122}{11}\)
\((4x+5):3=\dfrac{166}{11}\)
\((4x+5)=\dfrac{166}{11}\times3\)
\(4x+5=\dfrac{498}{11}\)
\(4x=\dfrac{498}{11}-5\)
\(4x=\dfrac{498}{11}-\dfrac{55}{11}\)
\(4x=\dfrac{498-55}{11}\)
\(4x=\dfrac{443}{11}\)
\(x=\dfrac{443}{11}:4\)
\(x=\dfrac{443}{11}.\dfrac{1}{4}\)
\(x=\dfrac{443}{44}\).
b) \(1+3+5+....+x=1600\)
\(\Rightarrow\left({\dfrac{x-1}{2}+1}\right)\left({\dfrac{x+1}{2}}\right)=1600\)
\(\Rightarrow\left({\dfrac{x-1}{2}+\dfrac{2}{2}}\right)\left({\dfrac{x+1}{2}}\right)=1600\)
\(\Rightarrow\left({\dfrac{x-1+2}{2}}\right)\left({\dfrac{x+1}{2}}\right)=1600\)
\(\Rightarrow\left({\dfrac{x+1}{2}}\right)\left({\dfrac{x+1}{2}}\right)=1600\)
\(\Rightarrow\left({\dfrac{x+1}{2}}\right)=40\)
\(\Rightarrow x+1=40.2\)
\(\Rightarrow x+1=80\)
\(\Rightarrow \) \(x=80-1\)
\(\Rightarrow\) \( x=79\).
