Equations and inequalities with parameters | math4u.vsb.cz

9000140005

Level:

C

Solve the following equation with unknown

x

and a real parameter

a \in R ∖ {0}

.

\frac{a}{x} - \frac{4}{a x} = 1 - \frac{2}{a}

\begin{array}{cc} Parameter & Solution set \\ a = - 2 & \emptyset \\ a = 2 & R ∖ {0} \\ a \notin {- 2; 0; 2} & {a + 2} \end{array}

\begin{array}{cc} Parameter & Solution set \\ a = 2 & R ∖ {0} \\ a \notin {0; 2} & {a + 2} \end{array}

\begin{array}{cc} Parameter & Solution set \\ a = 2 & R \\ a \notin {0; 2} & {a + 2} \end{array}

\begin{array}{cc} Parameter & Solution set \\ a = 2 & R ∖ {1} \\ a \notin {0; 2} & {a + 2} \end{array}