Equations and inequalities with parameters

2000019102

Level:

Determine the set of all values of the real parameter

a

for which the given equation has no solution.

a^{2} x = x + a

{- 1; 1}

{- 1; 0; 1}

{1}

{0; 1}

2000019103

Level:

Determine the set of all values of the parameter

a \in R ∖ {3}

for which the given equation has no solution.

\frac{5 x - 2}{a - 3} = 4 + \frac{2 x}{3}

{\frac{21}{2}}

{\frac{2}{5}}

{- 3}

{0}

2000019104

Level:

Consider the following equation with a parameter

a

5 x - a = a x + 4

Choose the table that summarizes solutions of the equation according to the value of

a

\begin{array}{cc} Parameter & Solution set \\ a = 5 & \emptyset \\ a \neq 5 & {\frac{a + 4}{5 - a}} \end{array}

\begin{array}{cc} Parameter & Solution set \\ a = 5 & R \\ a \neq 5 & {\frac{a + 4}{5 - a}} \end{array}

\begin{array}{cc} Parameter & Solution set \\ a = 5 & R \\ a \neq 5 & \emptyset \end{array}

2000019107

Level:

Determine the set of all values of the real parameter

a

for which the equation has an infinite number of solutions.

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

{1}

{- 1}

{0}

\emptyset

2000019108

Level:

Determine the set of all values of the parameter

a \in R ∖ {- 2; 2}

for which the equation has an infinite number of solutions.

\frac{x - a}{2 - a} = \frac{x + a}{2 + a}

{0}

{- 1}

{1}

\emptyset

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)

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)

2010008405

Level:

Consider the equation

x^{2} (1 - q) + 2 x + 1 + q = 0

with the real parameter

q

. Solve the equation for

q = - 1

{- 1; 0}

{- 1; 1}

{0; 1}

\emptyset

2010008406

Level:

Consider equation

q (3 - q) x = 6 - 2 q

with a real parameter

q

. Solve the equation for

q = 3

R

\emptyset

R ∖ {0}

{\frac{6 - 2 q}{q (3 - q)}}

2010008407

Level:

Determine the set of all values of the real parameter

a

for which the equation will have exactly one solution.

a^{2} x + 2 a x - 3 a = 0

R ∖ {0; - 2}

{0; \frac{1}{3}}

R ∖ {0; - 2}

R

Equations and inequalities with parameters

2000019102

2000019103

2000019104

2000019107

2000019108

2010008401

2010008402

2010008405

2010008406

2010008407

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