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Solving Linear Equations quiz

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  • What is the first step when solving any linear equation?
    The first step is to simplify both sides of the equation by distributing and combining like terms.
  • How do you eliminate parentheses in a linear equation?
    You eliminate parentheses by distributing the coefficient across the terms inside the parentheses.
  • What should you do after distributing and combining like terms in a linear equation?
    After simplifying, use addition or subtraction properties of equality to collect variable terms on one side and constants on the other.
  • How do you isolate the variable when it has a coefficient?
    Use multiplication or division properties of equality to solve for the variable by dividing or multiplying both sides by the coefficient.
  • Why is it important to check your solution after solving a linear equation?
    Checking your solution by substituting it back into the original equation ensures that it makes the equation true.
  • What is the purpose of multiplying both sides of an equation by the least common denominator (LCD) when fractions are present?
    Multiplying by the LCD clears all fractions from the equation, making it easier to solve.
  • How do you clear decimals from a linear equation before solving?
    Multiply both sides of the equation by a power of 10 that matches the highest number of decimal places in the equation.
  • What is a conditional equation in the context of linear equations?
    A conditional equation is true for exactly one value of the variable, meaning it has one solution.
  • What do you call a linear equation that is true for all values of the variable?
    Such an equation is called an identity and has infinite solutions.
  • What is a contradiction in linear equations?
    A contradiction is an equation that is never true, so it has no solutions.
  • What is the solution set of an identity equation?
    The solution set is all real numbers.
  • What is the solution set of a contradiction or inconsistent equation?
    The solution set is the empty set, meaning there are no solutions.
  • What does it mean to combine like terms in a linear equation?
    It means to add or subtract terms that have the same variable raised to the same power.
  • When solving an equation with fractions, what is step zero?
    Step zero is to clear the fractions by multiplying both sides by the least common denominator.
  • How do you determine which power of 10 to use when clearing decimals from an equation?
    Use the power of 10 that matches the highest number of decimal places in any term of the equation.