Equations with No Solutions Worksheet
Explore linear equations that have no solutions through various exercises including identifying, solving, and explaining the concept at a Grade 6 level.
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Equations with No Solutions
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Read each question carefully and follow the instructions. Show your work for all problems.
What is an Equation with No Solution?
An equation with no solution is an equation where no value for the variable will make the equation true. When you try to solve these equations, you will often end up with a false statement, like 0 = 5.
1. Which of the following equations has no solution?
x + 3 = 7
2x = 10
x + 5 = x + 1
3x - 1 = 8
2. What happens when you try to solve an equation with no solution?
You get a true statement, like 5 = 5.
You get a false statement, like 0 = 3.
You find a specific value for the variable.
The variable disappears, and you don't get a statement.
3. An equation with no solution means there is no that can make the equation true.
4. When solving an equation with no solution, the variables will from both sides.
5. Solve the following equation and determine if it has no solution, one solution, or infinitely many solutions. Explain your reasoning.
2x + 4 = 2x - 1
6. The equation 3x + 2 = 3x + 2 has no solution.
True
False
7. If an equation simplifies to 7 = 0, it has no solution.
True
False
8. Consider the balance scale below. If each 'x' represents an unknown weight and each square represents 1 unit of weight, draw what would happen if you tried to balance the equation x + 3 = x + 5.
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