Pregunta
For each equation, choose the statement that describes its solution.
If applicable, give the solution.
(a)
O No solution
O All real numbers are solutions
(b)
O
O All real numbers are solutions
If applicable, give the solution.
| (a)
|
| O No solution |
| O All real numbers are solutions |
| (b)
|
|
|
| O
|
| O All real numbers are solutions |
Ask by Dunn Tyler. in the United States
Jan 24,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
(a) All real numbers are solutions.
(b) No solution.
Solución
Let’s analyze each equation to determine their solutions.
(a)
Step-by-Step Solution:
-
Expand both sides:
-
Combine like terms:
-
Subtract
from both sides: -
Interpretation:
This simplifies to a true statement () regardless of the value of . This means every real number satisfies the equation.
Conclusion for (a):
- Statement: All real numbers are solutions.
- Solution: Every real number
is a solution.
(b)
Step-by-Step Solution:
-
Expand both sides:
-
Combine like terms:
-
Subtract
from both sides: -
Interpretation:
This simplifies to a false statement (), which means there is no solution to the equation.
Conclusion for (b):
- Statement: No solution.
- Solution: There is no value of
that satisfies the equation.
Final Answers:
- (a) All real numbers are solutions.
- (b) No solution.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Simplifique esta solución Mind Expander
Let’s tackle each equation one by one!
For equation (a)
First, simplify both sides:
LHS:
RHS:
Now, we have
First, simplify both sides:
LHS:
RHS:
Now, we have
For equation (b)
Expanding both sides yields:
LHS:
RHS:
Now, setting them equal gives
Expanding both sides yields:
LHS:
RHS:
Now, setting them equal gives
To summarize:
(a) All real numbers are solutions.
(b) No solution.
(a) All real numbers are solutions.
(b) No solution.
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