Equations with No Solutions Worksheet
Practice identifying and solving linear equations that have no solutions, understanding the properties that lead to such outcomes.
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Equations with No Solutions
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Read each question carefully and follow the instructions. Simplify each equation if possible. Determine if the equation has one solution, no solution, or infinitely many solutions. If there is no solution, explain why.
1. Which of the following equations has no solution?
3x + 5 = 3x - 2
2x + 7 = x + 7
4x - 1 = 2x + 3
5x + 1 = 5x + 1
2. Consider the equation: 6(x + 2) = 6x + 10. Does this equation have a solution?
Yes, one solution
No solution
Infinitely many solutions
Cannot be determined
3. An equation has no solution if, after simplifying, the variables cancel out and the remaining statement is .
4. In the equation 5x + 3 = 5x + 10, the terms with variables are , but the constant terms are .
5. Explain why the equation 2(x - 4) = 2x + 5 has no solution. Show your work.
6. Create an equation that has no solution. Justify your answer.
7. The equation 7x - 3 = 7x - 3 has no solution.
True
False
8. If an equation simplifies to 0 = 5, it means there is no solution.
True
False
9. A balance scale is shown below. If each 'x' represents an unknown weight and each circle represents a 1-pound weight, write an equation that represents a situation where the scale can never be balanced.
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