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Solving Linear Equations quiz

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  • What is the first step when solving a linear equation?
    The first step is to simplify both sides by distributing and combining like terms.
  • How do you combine like terms in a linear equation?
    Combine terms with the same variable or constants by adding or subtracting them.
  • What property is used to move variable terms to one side of the equation?
    The addition or subtraction property of equality is used to move variable terms.
  • How do you isolate the variable in the final step of solving a linear equation?
    Use multiplication or division properties of equality to solve for the variable.
  • Why should you check your solution after solving a linear equation?
    Checking ensures the solution makes the original equation a true statement.
  • What should you do if a linear equation contains fractions?
    Multiply both sides by the least common denominator to clear the fractions.
  • How do you clear decimals from a linear equation?
    Multiply both sides by a power of 10 based on the highest number of decimal places.
  • What is the solution to the equation 2x - 5 = 3 after clearing fractions?
    The solution is x = 4.
  • What is the solution to the equation 36 = 3x + 30 after clearing decimals?
    The solution is x = 2.
  • What is a conditional equation?
    A conditional equation has exactly one solution that makes the equation true.
  • What is an identity equation?
    An identity equation is always true and has infinite solutions; any value for x works.
  • What is a contradiction or inconsistent equation?
    A contradiction equation is always false and has no solutions.
  • How can you represent the solution set of an identity equation?
    The solution set is all real numbers, often written as ℝ or in set builder notation.
  • What symbol represents the empty set for a contradiction equation?
    The empty set is represented by {} or a zero with a line through it (∅).
  • What are the four main steps for solving a linear equation after clearing fractions or decimals?
    Simplify, collect variable and constant terms, isolate the variable, and check the solution.