First-Degree Equations

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Questions and Answers

What is the general form of a first-degree equation?

  • ax + b = 0 (correct)
  • ax + by = c
  • a/x + b = c
  • ax^2 + bx + c = 0

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

  • x = 2
  • x = -6
  • x = -2 (correct)
  • x = 6

Which of the following is a valid step in solving the equation 4(x + 3) = 2x - 5?

  • Combine like terms first and then distribute 4
  • Distribute 4 and then combine like terms (correct)
  • Combine like terms first and then add 3 to both sides
  • Distribute 4 and then add 3 to both sides

What is the first step in solving the equation 3x - 7 = 2x + 5?

<p>Add 7 to both sides (A)</p> Signup and view all the answers

What is the solution to the equation 2(3x - 4) = 5x + 6?

<p>x = 2 (D)</p> Signup and view all the answers

Which of the following is a valid step in solving the equation 4x - 8 = 2(3x + 1)?

<p>Distribute the 2 on the right side (A)</p> Signup and view all the answers

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Study Notes

First-Degree Equations

  • A first-degree equation, also known as a linear equation, is represented in the form Ax + B = C, where A, B, and C are constants and x is the variable.

Solution to Specific Equations

  • The solution to the equation 2x - 5 = 3x + 1 is found by isolating x, resulting in x = -6.
  • For the equation 3x - 7 = 2x + 5, the first step is typically to rearrange it to isolate x, usually by subtracting 2x from both sides, yielding x - 7 = 5.

Valid Steps in Solving Equations

  • In solving the equation 4(x + 3) = 2x - 5, distributing the 4 on the left side is a valid first step.
  • In the equation 4x - 8 = 2(3x + 1), a valid step includes distributing 2 on the right side, transforming it to 4x - 8 = 6x + 2.

Additional Solutions

  • The equation 2(3x - 4) = 5x + 6 simplifies by distributing 2, leading to 6x - 8 = 5x + 6, which can be solved to find x = 14.

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