Equations with Infinite and No Solutions
Explore linear equations that result in infinite solutions or no solutions, understanding their algebraic properties and graphical interpretations.
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Equations with Infinite and No Solutions
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Read each question carefully and solve for the variable. Determine if the equation has one solution, no solution, or infinite solutions. Show all your work.
1. Solve the equation: 3(x + 2) = 3x + 6
2. Solve the equation: 5x - 10 = 5(x - 3)
3. Solve the equation: 2(4x - 1) = 8x + 5
4. Which of the following equations has no solution?
2x + 5 = 2x + 5
3x - 4 = 3x + 1
4x - 7 = x + 2
5(x + 1) = 5x + 5
5. An equation with infinite solutions is also known as a(n):
Contradiction
Identity
Conditional equation
Linear equation
6. An equation has solutions if simplifying both sides results in a true statement, such as 0 = 0.
7. An equation has solutions if simplifying both sides results in a false statement, such as 0 = 5.
8. When solving an equation, if the variables cancel out and the remaining numbers are equal, the equation has solutions.
9. If an equation simplifies to 7 = 7, it has no solution.
True
False
10. Parallel lines on a graph represent a system of equations with no solution.
True
False
11. Explain in your own words the difference between an equation with no solution and an equation with infinite solutions. Provide an example of each.