Questions and Answers
5 − 2𝑥 = 2𝑥 − 5 This equation has _______ solution.
one
9(3𝑥 − 5) = 9(3𝑥 + 5) This equation has _____ solution.
no
6(2𝑥 + 4) = 3(4𝑥 + 8) This equation has _____ solutions.
Infinite
6𝑥 − 7 = −7 + 6x This equation has _____ _______.
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3𝑥 + 4 = −4 + 3x This equation has ____ _____.
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9𝑥 + 4 = 7𝑥 + 4 This equation has _____ _____.
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Solve for x: 2𝑥 + 7 = 7 + x
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Solve for x: 6 − 3𝑥 = 3𝑥 − 6
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Solve for x: 3(2𝑥 + 1) = 2(2𝑥 + 1)
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Solve for x: 6𝑥 − 8 = 8 − 6x
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Solve for x: 6𝑥 − 12 = 8 − 3𝑥
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Solve for x: 3(𝑥 − 1) = 2(2x − 1) + 2
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Study Notes
One Solution
- An equation with one solution has a unique value for the variable that satisfies it.
- Example: The equation 5 − 2𝑥 = 2𝑥 − 5 results in one solution.
No Solution
- An equation with no solution has no values of the variable that can satisfy it, indicating a contradiction.
- Example: The equation 9(3𝑥 − 5) = 9(3𝑥 + 5) results in no solution.
Infinite Solutions
- An equation that results in infinite solutions means that the equation is true for all values of the variable.
- Example: The equation 6(2𝑥 + 4) = 3(4𝑥 + 8) yields infinite solutions.
Infinite Solutions Specific Case
- The equation 6𝑥 − 7 = −7 + 6x demonstrates infinite solutions since it simplifies to an identity.
No Solution Specific Case
- The equation 3𝑥 + 4 = −4 + 3x is an example that leads to no solution, presenting a contradiction.
One Solution Specific Case
- The equation 9𝑥 + 4 = 7𝑥 + 4 results in one solution, indicating a specific value for x.
Solving for x
- x = 0 can be derived from the equation 2𝑥 + 7 = 7 + x.
- x = 2 is the solution for the equation 6 − 3𝑥 = 3𝑥 − 6.
- For the equation 3(2𝑥 + 1) = 2(2𝑥 + 1), the solution is x = -1/2.
- The equation 6𝑥 − 8 = 8 − 6x results in x = 4/3.
- The solution for 6𝑥 − 12 = 8 − 3x is x = 20/9.
- The equation 3(𝑥 − 1) = 2(2x − 1) + 2 gives the solution x = -3.
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Description
Explore the intriguing world of algebra through flashcards that focus on equations with one solution, no solution, or infinite solutions. This quiz helps develop a deeper understanding of how to classify different types of equations and their solutions.
