Podcast
Questions and Answers
5 − 2𝑥 = 2𝑥 − 5 This equation has _______ solution.
5 − 2𝑥 = 2𝑥 − 5 This equation has _______ solution.
one
9(3𝑥 − 5) = 9(3𝑥 + 5) This equation has _____ solution.
9(3𝑥 − 5) = 9(3𝑥 + 5) This equation has _____ solution.
no
6(2𝑥 + 4) = 3(4𝑥 + 8) This equation has _____ solutions.
6(2𝑥 + 4) = 3(4𝑥 + 8) This equation has _____ solutions.
Infinite
6𝑥 − 7 = −7 + 6x This equation has _____ _______.
6𝑥 − 7 = −7 + 6x This equation has _____ _______.
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3𝑥 + 4 = −4 + 3x This equation has ____ _____.
3𝑥 + 4 = −4 + 3x This equation has ____ _____.
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9𝑥 + 4 = 7𝑥 + 4 This equation has _____ _____.
9𝑥 + 4 = 7𝑥 + 4 This equation has _____ _____.
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Solve for x: 2𝑥 + 7 = 7 + x
Solve for x: 2𝑥 + 7 = 7 + x
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Solve for x: 6 − 3𝑥 = 3𝑥 − 6
Solve for x: 6 − 3𝑥 = 3𝑥 − 6
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Solve for x: 3(2𝑥 + 1) = 2(2𝑥 + 1)
Solve for x: 3(2𝑥 + 1) = 2(2𝑥 + 1)
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Solve for x: 6𝑥 − 8 = 8 − 6x
Solve for x: 6𝑥 − 8 = 8 − 6x
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Solve for x: 6𝑥 − 12 = 8 − 3𝑥
Solve for x: 6𝑥 − 12 = 8 − 3𝑥
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Solve for x: 3(𝑥 − 1) = 2(2x − 1) + 2
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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.
