Equations with Infinite and No Solutions
Explore linear equations that result in infinite solutions (identities) or no solutions (contradictions) at a Grade 12 level.
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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 solutions, or infinitely many solutions. Show all your work.
1. Which of the following equations has infinitely many solutions?
3x + 5 = 3x - 2
2(x + 4) = 2x + 8
5x - 10 = 2x + 5
x/2 + 3 = x/2 - 1
2. An equation that has no solution is called a/an:
Identity
Contradiction
Conditional equation
Linear equation
3. An equation like 4x + 7 = 4x + 7 is an because it has many solutions.
4. If an equation simplifies to a false statement, such as 0 = 5, then it has solutions.
5. Solve the following equation and classify it as having one solution, no solution, or infinitely many solutions: 6(x - 2) + 10 = 6x - 2
6. Solve the following equation and classify it: 3(2x + 1) - 5 = 6x - 2
7. Solve the following equation and classify it: 5x - (2x + 3) = 3x - 3
8. An equation that simplifies to 0 = 0 has no solution.
True
False
9. If an equation has the same variable terms on both sides but different constant terms, it will have one solution.
True
False
10. For what value of 'k' would the equation 2(3x + 4) = kx + 8 have infinitely many solutions?
11. For what value of 'm' would the equation 5x - 7 = mx + 3 have no solution?