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College Algebra: Solving Linear Equations

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Terms in this set (10)

  • What is the first step in solving a linear equation?
    Distribute constants to remove parentheses.
  • After distributing constants, what is the next step in solving linear equations?
    Combine like terms on each side of the equation.
  • How do you arrange terms when solving linear equations?
    Group terms with x on one side and constants on the opposite side.
  • What does it mean to isolate x in a linear equation?
    Manipulate the equation so that x is alone on one side.
  • Why should you check your solution after solving a linear equation?
    To verify the solution by substituting x back into the original equation.
  • How do you solve linear equations that contain fractions?
    Multiply both sides by the Least Common Denominator (LCD) to eliminate fractions.
  • What is the purpose of multiplying by the LCD in equations with fractions?
    To clear fractions and simplify the equation for easier solving.
  • What does it mean if a linear equation simplifies to a false statement like \(0=5\)?
    The equation has no solution.
  • What does it mean if a linear equation simplifies to a true statement like \(0=0\)?
    The equation has infinitely many solutions.
  • How do you combine like terms in an equation?
    Add or subtract terms with the same variable and exponent.