Questions and Answers
What is the solution to the equation x - 7 = 25?
32
What is the solution to the equation 3x + 12 = -3?
-5
What is the solution to the equation 5 - 3x = -10?
5
What is the solution to the equation 3x - 30 = 0?
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What is the solution to the equation 3x + 4 = 25?
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What is the solution to the equation 5(x + 2) = 40?
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What is the solution to the equation 2(x + 2) = 2?
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What is the solution to the equation 7(x - 4) = -7?
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What is the solution to the equation -4x + 5 = -2x - 7?
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What is the solution to the equation 12x - 9 = 2x + 11?
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What is the solution to the equation 2x + 9 = x - 4?
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What is the solution to the equation 3x - 7 = 5x - 9?
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What is the solution to the equation 3(5x - 2) + 2 = 26?
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What is the solution to the equation 5(n + 2) = 3n?
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What is the solution to the equation 5(5 - x) = -5?
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What is the solution to the equation 1 + 4(2x + 1) = 5?
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What is the solution to the equation x + 3 = 3(11 - 3x)?
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What is the solution to the equation 5x - 7 = 13?
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What is the solution to the equation 2x - 4 = -4(x - 5)?
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What is the solution to the equation 3x = 2(7 + 5x)?
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What is the solution to the equation 2(3x + 1) = 7x - 5?
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What is the solution to the equation 2(x + 1) = 6x - 46?
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What is the solution to the equation 7(2 - x) - 5 = 30?
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What is the solution to the equation 5(x - 6) = 3 + 8(x + 9)?
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What is the solution to the equation 245 = -5(4x - 17)?
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What is the solution to the equation 17(3x + 2) = -272?
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What is the solution to the equation 5(7x - 13) = -30?
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What is the solution to the equation 12(-2x - 9) = -12?
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What is the solution to the equation -10(-4x + 7) = 130?
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What is the solution to the equation -210 = -7(9x - 60)?
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What is the solution to the equation 12(-x + 5) = 144?
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What is the solution to the equation 9(-4x - 29) = 99?
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Write a two-step equation so that x = 4.
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Write a two-step equation with parentheses so that x = 5.
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Study Notes
Solving Linear Equations in Algebra
- Mastery of solving linear equations involves manipulating equations to isolate the variable.
- Equations may include constants, coefficients, and operations like addition, subtraction, multiplication, or division.
Examples with Solutions
- x - 7 = 25: Leads to x = 32.
- 3x + 12 = -3: Simplifies to x = -5.
- 5 - 3x = -10: Results in x = 5.
- 3x - 30 = 0: Yields x = 10.
Variability in Equation Forms
- Varying the structure of equations:
- 3x + 4 = 25: Solves to x = 7.
- 5(x + 2) = 40: Solves to x = 6.
- 2(x + 2) = 2: Simplifies to x = -1.
Working with Different Variables
- Equations involving negative and fractional coefficients can also be solved:
- -4x + 5 = -2x - 7: Results in x = 2.
- 12x - 9 = 2x + 11: Yields x = 2.
Strategy for Checking Solutions
- Ensure solutions are verified by substituting back into the original equation.
- An example: For 5(n + 2) = 3n, if calculated as x = -5, substitute to check consistency.
Creating Two-Step Equations
- Formulate two-step equations for a predetermined solution:
- For x = 4, an example would be 2x - 3 = 5.
- For x = 5, use 2(x + 3) = 16.
Summary of Variable Isolation
- Solve for x by performing inverse operations on both sides to isolate the variable effectively.
- Aim for clarity during simplification to avoid common mistakes such as sign errors or miscalculations.
Highlight on Negative Solutions
- Understand that linear equations can yield both positive and negative solutions:
- Example: 5(7x - 13) = -30 results in x = 1, demonstrating a possible scenario of modifying coefficients to shape outcomes.
Utilize these notes to enhance understanding and practice solving equations effectively.
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Test your knowledge of solving equations with our Algebra 1 review flashcards. Each card presents a different equation for you to solve, helping you reinforce your understanding of algebraic concepts and skills. Perfect for last-minute revision or mastering specific topics!
