Equations with No Solutions
Explore linear equations that have no solutions, understanding their properties and how to identify them.
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Equations with No Solutions
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Read each question carefully and follow the instructions. Show all your work for short answer questions.
1. Which of the following equations has no solution?
2x + 5 = 2x + 5
3x - 7 = 3x + 2
4x + 1 = 9
5x - 10 = 2x + 5
2. An equation has no solution if, after simplifying both sides, you get:
A true statement (e.g., 5 = 5)
A false statement (e.g., 3 = 7)
A variable equal to a number (e.g., x = 4)
An inequality (e.g., x > 2)
3. An equation with no solution will result in a statement when simplified.
4. In an equation with no solution, the variable terms on both sides of the equation will .
5. The equation 6x - 1 = 6x + 4 has infinitely many solutions.
True
False
6. If an equation simplifies to 0 = 5, then it has no solution.
True
False
7. Explain in your own words what it means for an equation to have “no solution”.
8. Simplify the following equation and determine if it has no solution. Show your work: 3(2x + 1) - 4x = 2x + 5
9. Consider the balance scale below. If each 'x' represents an unknown weight and each block is a known weight, what would happen if you tried to balance 2x + 3 on one side and 2x + 5 on the other? Explain why this represents an equation with no solution.
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