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College Algebra: Solving Linear Equations

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  • 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 the variable on one side and constants on the opposite side.
  • What does it mean to isolate the variable in a linear equation?
    Manipulate the equation so that the variable is alone on one side.
  • Why should you check your solution after solving a linear equation?
    To verify the solution by substituting the variable back into the original equation.
  • How do you handle fractions in linear equations?
    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 are the three possible categories of linear equations based on their solutions?
    One solution, no solution, or infinitely many solutions.
  • How can solutions of linear equations be expressed?
    Solutions may be written as a single value, no solution, or all real numbers.
  • What is the solution to the equation 2(x - 3) = 0?
    x = 3
  • What is the first step to solve 3(2 - 5x) = 4x + 25?
    Distribute 3 to both terms inside the parentheses.
  • What should you do after grouping terms with variables and constants on opposite sides?
    Isolate the variable by adding or subtracting terms.
  • What is the recommended step to solve 1/4(x + 2) - 1/3 x = 1/12?
    Multiply both sides by 12, the LCD, to eliminate fractions.
  • What does combining like terms involve?
    Adding or subtracting terms with the same variable or constants.
  • What is the final step in solving linear equations before checking the solution?
    Solve for the variable by isolating it completely.
  • Why is it optional but recommended to check your solution?
    To confirm the solution satisfies the original equation.
  • What does it mean if a linear equation has no solution?
    The equation is inconsistent and the lines are parallel.
  • What does it mean if a linear equation has infinitely many solutions?
    The equation is an identity; both sides are equivalent for all variable values.
  • What is the role of constants in solving linear equations?
    Constants are moved to one side to isolate the variable.
  • What is a linear equation?
    An equation where the variable is to the first power and graphs as a straight line.