Math Problem Statement
Solution
Let's analyze each of the given equations to determine which one has no solution. An equation with no solution typically occurs when simplifying leads to a contradiction like , where .
1.
Expand both sides: Subtract from both sides: This is a contradiction. Therefore, this equation has no solution.
2.
Expand the right side: Simplify: This is always true, so this equation has infinitely many solutions.
3.
Expand both sides: Simplify: Subtract from both sides: Add to both sides: Solve for : This equation has one solution, .
4.
Expand both sides: Subtract from both sides: Subtract from both sides: Solve for : This equation has one solution, .
Conclusion:
The equation that has no solution is: This is the first equation, as it leads to the contradiction .
Do you want more details or have any questions?
Here are five related questions to explore:
- What does it mean for an equation to have no solution?
- How do you identify when an equation has infinitely many solutions?
- What types of equations typically result in a single solution?
- How can you graphically represent an equation with no solution?
- Why does subtracting the same term from both sides help simplify an equation?
Tip: Always double-check for contradictions or true statements when simplifying an equation. This will help identify whether the equation has no solution or infinitely many solutions.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Contradictions in Algebra
Formulas
Distributive Property: a(b + c) = ab + ac
Equation Simplification: ax + b = cx + d
Theorems
If a statement like a = b (where a ≠ b) is reached, the equation has no solution.
Suitable Grade Level
Grades 7-9