Pregunta
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
To make the equation
- No values of
: Use any constant different from 8, e.g., . - All values of
: Use the same constant as on the left, e.g., . - One value of
: Use an expression involving , e.g., .
Solución
Certainly! Let’s analyze the equation and determine appropriate values to place after
Given Equation:
We need to choose a suitable [value] such that:
- No values of
satisfy the equation. - All values of
satisfy the equation. - Only one specific value of
satisfies the equation.
Let’s explore each scenario in detail.
1. No Values of
Objective: Make the equation false for all possible values of
Approach:
- Substitute [value] with a constant that is different from the constant term on the left side.
- This creates a contradiction, making the equation unsolvable.
Example:
Explanation:
- Subtract
from both sides: - This is a false statement, meaning there’s no solution.
General Rule:
Set [value] to any constant not equal to 8.
Set [value] to any constant not equal to 8.
2. All Values of
Objective: Make the equation always true, regardless of the value of
Approach:
- Substitute [value] with the same constant that’s on the left side.
- This ensures both sides of the equation are identical.
Example:
Explanation:
- Subtract
from both sides: - This is always true, meaning all values of
are solutions.
General Rule:
Set [value] to 8.
Set [value] to 8.
3. Only One Specific Value of
Objective: Make the equation true for exactly one value of
Approach:
- Substitute [value] with an expression involving
. - This introduces an additional variable, allowing the equation to be solvable for a unique
.
Example:
Simplify and Solve:
Explanation:
- The equation simplifies to
, meaning only satisfies the equation.
Another Example:
Simplify and Solve:
Explanation:
- The equation simplifies to
, meaning only satisfies the equation.
General Rule:
Set [value] to an expression of the form
Set [value] to an expression of the form
Summary
-
No Solution:
(Any constant not equal to 8) -
All Solutions:
(The constant 8) -
One Solution:
(An expression involving, such as )
By appropriately choosing the [value], you can control the nature of the solutions to the equation.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg
Explicar 
Simplifique esta solución Bonus Knowledge
To make the equation true for no values of
For the case of all values of
To make the equation true for just one value of
preguntas relacionadas
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
