Algebra 1 Equations Review Flashcards
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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?

<p>10</p> Signup and view all the answers

What is the solution to the equation 3x + 4 = 25?

<p>7</p> Signup and view all the answers

What is the solution to the equation 5(x + 2) = 40?

<p>6</p> Signup and view all the answers

What is the solution to the equation 2(x + 2) = 2?

<p>-1</p> Signup and view all the answers

What is the solution to the equation 7(x - 4) = -7?

<p>3</p> Signup and view all the answers

What is the solution to the equation -4x + 5 = -2x - 7?

<p>2</p> Signup and view all the answers

What is the solution to the equation 12x - 9 = 2x + 11?

<p>2</p> Signup and view all the answers

What is the solution to the equation 2x + 9 = x - 4?

<p>-13</p> Signup and view all the answers

What is the solution to the equation 3x - 7 = 5x - 9?

<p>1</p> Signup and view all the answers

What is the solution to the equation 3(5x - 2) + 2 = 26?

<p>2</p> Signup and view all the answers

What is the solution to the equation 5(n + 2) = 3n?

<p>-5</p> Signup and view all the answers

What is the solution to the equation 5(5 - x) = -5?

<p>6</p> Signup and view all the answers

What is the solution to the equation 1 + 4(2x + 1) = 5?

<p>0</p> Signup and view all the answers

What is the solution to the equation x + 3 = 3(11 - 3x)?

<p>3</p> Signup and view all the answers

What is the solution to the equation 5x - 7 = 13?

<p>4</p> Signup and view all the answers

What is the solution to the equation 2x - 4 = -4(x - 5)?

<p>4</p> Signup and view all the answers

What is the solution to the equation 3x = 2(7 + 5x)?

<p>-2</p> Signup and view all the answers

What is the solution to the equation 2(3x + 1) = 7x - 5?

<p>7</p> Signup and view all the answers

What is the solution to the equation 2(x + 1) = 6x - 46?

<p>12</p> Signup and view all the answers

What is the solution to the equation 7(2 - x) - 5 = 30?

<p>-3</p> Signup and view all the answers

What is the solution to the equation 5(x - 6) = 3 + 8(x + 9)?

<p>-35</p> Signup and view all the answers

What is the solution to the equation 245 = -5(4x - 17)?

<p>-8</p> Signup and view all the answers

What is the solution to the equation 17(3x + 2) = -272?

<p>-6</p> Signup and view all the answers

What is the solution to the equation 5(7x - 13) = -30?

<p>1</p> Signup and view all the answers

What is the solution to the equation 12(-2x - 9) = -12?

<p>-4</p> Signup and view all the answers

What is the solution to the equation -10(-4x + 7) = 130?

<p>5</p> Signup and view all the answers

What is the solution to the equation -210 = -7(9x - 60)?

<p>10</p> Signup and view all the answers

What is the solution to the equation 12(-x + 5) = 144?

<p>-7</p> Signup and view all the answers

What is the solution to the equation 9(-4x - 29) = 99?

<p>-10</p> Signup and view all the answers

Write a two-step equation so that x = 4.

<p>2x - 3 = 5</p> Signup and view all the answers

Write a two-step equation with parentheses so that x = 5.

<p>2(x + 3) = 16</p> Signup and view all the answers

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!

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