Equations and inequalities with parameters

2010008402

Level:

Find all the values of the parameter

k

so that the solution of the following equation is positive.

k x - 2 = 3 x - k

k \in (2; 3)

k \in (0; \infty)

k \in (3; \infty)

k \in (- \infty; 2)

2010008401

Level:

Find all the values of the parameter

k

so that the solution of the following equation is bigger than

6

2 x - 9 = \frac{7 x - 3 k}{3}

k \in (- \infty; 11)

k \in {11}

k \in (11; \infty)

k \in (- \infty; 13)

Quadratic Equations with Parameters

Submitted by ladislav.foltyn on Sat, 04/20/2019 - 13:43

Absolute Value Equations with Parameter

Submitted by ladislav.foltyn on Sat, 03/02/2019 - 15:56

9000375401

Level:

Find a set of the values of the real parameter

a

which ensure that the following equation has a unique solution.

a^{3} x + 4 a - 1 = a^{2} x + 3

R ∖ {0; 1}

R ∖ {- 1; 1}

R ∖ {0}

R ∖ {- 1; 0}

9000375402

Level:

Find a set of the values of the real parameter

a

which ensure that the following equation does not have a solution.

2 x + a = a (a^{2} - x)

{- 2}

{1}

{- 1}

{0}

9000375403

Level:

Find a set of the values of the real parameter

a

which ensure that the following equation has infinitely many solutions.

a^{2} x + a x - a = 2 x - 1

{1}

\emptyset

{0}

{- 2}

9000375404

Level:

Find a set of the values of the real parameter

a

which ensure that the following equation has infinitely many solutions.

a^{2} x + 2 a x - 3 x = a - 2

\emptyset

{- 3; 1}

{- 3; 1; 2}

{0}

9000375405

Level:

Find a set of the values of the real parameter

a

which ensure that the following equation has a unique solution.

a^{2} x + 6 x = a + 1 - 5 a x

R ∖ {- 3; - 2}

R ∖ {2; 3}

R ∖ {- 1; 2; 3}

R ∖ {- 3; - 2; 1}

9000140004

Level:

Solve the following equation with unknown

x

and a real parameter

a \in R

\frac{a^{2} (x - 1)}{a x - 3} = 3

\begin{array}{cc} Parameter & Solution set \\ a = 0 & \emptyset \\ a = 3 & R ∖ {1} \\ a \notin {0; 3} & {\frac{a + 3}{a}} \end{array}

\begin{array}{cc} Parameter & Solution set \\ a = 0 & \emptyset \\ a = 3 & {1} \\ a \notin {0; 3} & {\frac{a + 3}{a}} \end{array}

\begin{array}{cc} Parameter & Solution set \\ a \in {0; 3} & \emptyset \\ a \notin {0; 3} & {\frac{a + 3}{a}} \end{array}

\begin{array}{cc} Parameter & Solution set \\ a = 0 & \emptyset \\ a = 3 & R \\ a \notin {0; 3} & {\frac{a + 3}{a}} \end{array}

Equations and inequalities with parameters

2010008402

2010008401

Quadratic Equations with Parameters

Absolute Value Equations with Parameter

9000375401

9000375402

9000375403

9000375404

9000375405

9000140004

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