Math Problem Statement
Jubal wrote the four equations below. He examined them, without solving them, to determine which equation has no solution.
Which of Jubal’s equations has no solution? 7x+1=7x+1, 3x+2=3x-2, 4x+1=3x+8, -2x-1=-2x-1,
Solution
To determine which of Jubal's equations has no solution, we can analyze each equation.
-
Equation:
Simplifying, we subtract from both sides:
This is always true, so this equation has infinitely many solutions. -
Equation:
Simplifying, we subtract from both sides:
This is never true, so this equation has no solution. -
Equation:
Simplifying, we subtract from both sides:
Subtracting 1 from both sides gives:
This equation has a single solution . -
Equation:
Simplifying, we add to both sides:
This is always true, so this equation has infinitely many solutions.
Conclusion: The equation that has no solution is .
Would you like more details or have any other questions?
Here are 5 related questions:
- What does it mean for an equation to have no solution?
- How do you determine if an equation has infinitely many solutions?
- Can an equation have exactly two solutions? Why or why not?
- What are the steps to solve a linear equation?
- What is the difference between a consistent and inconsistent system of equations?
Tip: When comparing both sides of an equation, if the variables cancel out and you end up with a false statement (like ), the equation has no solution.
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Math Problem Analysis
Mathematical Concepts
Equations
Solution analysis
Infinite solutions
No solution
Formulas
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Theorems
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Suitable Grade Level
High school
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