Equations and inequalities with parameters

9000140002

Level: 
A
Solve the following equation with unknown x and a real parameter a∈R∖{0}. x+aa=ax−1
ParameterSolution seta∈{−1;1}∅a∉{−1;0;1}{2a(a−1)(a+1)}
ParameterSolution seta=−1∅a∉{−1;0}{2a(a−1)(a+1)}
ParameterSolution seta∈{−1;1}Ra∉{−1;0;1}{2a(a−1)(a+1)}

9000140003

Level: 
A
Solve the following equation with unknown x and a real parameter a∈R∖{0}. ax−2a2=4x+1a
ParameterSolution seta=−2Ra=2∅a∉{−2;0;2}{1a(a−2)}
ParameterSolution seta=−2R∖{1}a=2∅a∉{−2;0;2}{1a(a−2)}
ParameterSolution seta=−2∅a=2Ra∉{−2;0;2}{1a(a−2)}

9000140004

Level: 
C
Solve the following equation with unknown x and a real parameter a∈R. a2(x−1)ax−3=3
ParameterSolution seta=0∅a=3R∖{1}a∉{0;3}{a+3a}
ParameterSolution seta=0∅a=3{1}a∉{0;3}{a+3a}
ParameterSolution seta∈{0;3}∅a∉{0;3}{a+3a}
ParameterSolution seta=0∅a=3Ra∉{0;3}{a+3a}

9000140005

Level: 
C
Solve the following equation with unknown x and a real parameter a∈R∖{0}. ax−4ax=1−2a
ParameterSolution seta=−2∅a=2R∖{0}a∉{−2;0;2}{a+2}
ParameterSolution seta=2R∖{0}a∉{0;2}{a+2}
ParameterSolution seta=2Ra∉{0;2}{a+2}
ParameterSolution seta=2R∖{1}a∉{0;2}{a+2}