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Questions and Answers
What is the best interpretation of the solution when a linear equation results in a variable expression set equal to the same variable expression?
What is the best interpretation of the solution when a linear equation results in a variable expression set equal to the same variable expression?
The equation has infinite solutions.
How many solutions exist for the given equation: $\frac{1}{2}(x + 12) = 4x - 1$?
How many solutions exist for the given equation: $\frac{1}{2}(x + 12) = 4x - 1$?
one
What is the value of x in the equation $\frac{1}{2}x (x - 14) + 11 = \frac{1}{2}x - (x - 4)$?
What is the value of x in the equation $\frac{1}{2}x (x - 14) + 11 = \frac{1}{2}x - (x - 4)$?
0
What is the value of x in the equation $1.5(x + 4) - 3 = 4.5(x - 2)$?
What is the value of x in the equation $1.5(x + 4) - 3 = 4.5(x - 2)$?
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How many solutions exist for the given equation: $12x + 1 = 3(4x + 1) - 2$?
How many solutions exist for the given equation: $12x + 1 = 3(4x + 1) - 2$?
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Solve for x in the equation $9(x + 1) = 25 + x$.
Solve for x in the equation $9(x + 1) = 25 + x$.
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Which equation has no solution?
Which equation has no solution?
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Solve for n in the equation $n + 1 = 4(n - 8)$.
Solve for n in the equation $n + 1 = 4(n - 8)$.
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How many solutions exist for the equation: $0.75(x + 40) = 0.35(x + 20) + 0.35(x + 20)$?
How many solutions exist for the equation: $0.75(x + 40) = 0.35(x + 20) + 0.35(x + 20)$?
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How many solutions exist for the equation: $3(x - 2) = 22 - x$?
How many solutions exist for the equation: $3(x - 2) = 22 - x$?
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Solve for x in the equation $6(x - 1) = 9(x + 2)$.
Solve for x in the equation $6(x - 1) = 9(x + 2)$.
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What is the best interpretation when the equation $\frac{2}{3}(6x - 3) = \frac{1}{2}(6x - 4)$ simplifies to $4x = 3x$?
What is the best interpretation when the equation $\frac{2}{3}(6x - 3) = \frac{1}{2}(6x - 4)$ simplifies to $4x = 3x$?
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What is the value of x in the equation $2.5(6x - 4) = 10 + 4(1.5 + 0.5x)$?
What is the value of x in the equation $2.5(6x - 4) = 10 + 4(1.5 + 0.5x)$?
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How can Lily's partial solution from the equation $4(x - 1) - x = 3(x + 5) - 11$ be interpreted?
How can Lily's partial solution from the equation $4(x - 1) - x = 3(x + 5) - 11$ be interpreted?
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What is the value of n in the equation $\frac{1}{2}(n - 4) - 3 = 3 - (2n + 3)$?
What is the value of n in the equation $\frac{1}{2}(n - 4) - 3 = 3 - (2n + 3)$?
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How many solutions exist for the equation $3x + 13 = 3(x + 6) + 1$?
How many solutions exist for the equation $3x + 13 = 3(x + 6) + 1$?
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What is the value of x in the equation $1.5(x + 4) - 3 = 4.5(x - 2)$?
What is the value of x in the equation $1.5(x + 4) - 3 = 4.5(x - 2)$?
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Solve for x in the equation $5(x - 10) = 30 - 15x$.
Solve for x in the equation $5(x - 10) = 30 - 15x$.
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Study Notes
Infinite Solutions
- If a linear equation simplifies to the same variable expression on both sides, it has infinite solutions.
Unique Solutions
- The equation ( \frac{1}{2}(x + 12) = 4x - 1 ) has one solution.
- The equation ( 0.75(x + 40) = 0.35(x + 20) + 0.35(x + 20) ) results in one solution.
- The equation ( 3(x - 2) = 22 - x ) also results in one solution.
Solution Equations
- For the equation ( \frac{1}{2}x(x - 14) + 11 = \frac{1}{2}x - (x - 4) ), the solution leads to ( x = 0 ) after simplification.
- The value of ( x ) in the equation ( 1.5(x + 4) - 3 = 4.5(x - 2) ) is found to be 4.
- Solving ( 9(x + 1) = 25 + x ) results in ( x = 2 ).
- ( n + 1 = 4(n - 8) ) simplifies to ( n = 11 ).
No Solution
- The equation ( 5 + 2(3 + 2x) = x + 3(x + 1) ) has no solution.
- Interpretation of ( 4(x - 1) - x = 3(x + 5) - 11 ) indicates no solution.
Solutions Leading to Contradictions
- The equation ( 6(x - 1) = 9(x + 2) ) simplifies to ( x = -8 ).
- The equation ( 3x + 13 = 3(x + 6) + 1 ) yields zero solutions and indicates a contradiction.
Additional Key Values
- For the equation ( 1.5(x + 4) - 3 = 4.5(x - 2) ), the solution for ( x ) is confirmed as 4 again.
- In ( 5(x - 10) = 30 - 15x ), solving gives ( x = 4 ).
Summary of Solutions
- Equations can lead to infinite solutions, unique solutions, or no solutions based on their structure and simplification. Ensure to analyze the equations for potential contradictions or consistent identities.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of linear equations and the distributive property through these flashcards. Each card presents a scenario or question that will challenge your knowledge and interpretation of solutions. Perfect for reinforcing your skills in algebra!
