Math Problem Statement
Solution
Let's solve the equations step by step to determine whether each has one solution, no solution, or infinite solutions.
Part (a):
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Expand the left-hand side: So the equation becomes:
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Move all -terms to one side and constants to the other: Subtract from both sides: Add to both sides:
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Solve for :
Conclusion: The equation has one solution, .
Part (b):
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Expand the left-hand side: So the equation becomes:
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Simplify: Subtract from both sides:
Conclusion: The equation is always true. Therefore, it has infinite solutions.
Final Answer:
- (a) One solution:
- (b) Infinite solutions
Do you want details on any step or further explanations?
Here are 5 related questions to expand your understanding:
- What are the general steps to identify if an equation has one solution, no solution, or infinite solutions?
- How do you handle equations with fractions?
- What happens when variable terms cancel out entirely, leaving just numbers?
- How can you verify your solution by substitution?
- What are the key differences between equations and identities?
Tip: Always simplify both sides of an equation fully before deciding on the solution type.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Simplification of Equations
Formulas
Properties of equality (e.g., adding, subtracting, multiplying, and dividing both sides)
Theorems
Identity property (e.g., a = a)
No-solution property for inconsistent equations
Suitable Grade Level
Grade 8
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