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Solving Linear Equations 7th may

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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 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 satisfies the original equation by substitution.
  • How do you solve linear equations that contain fractions?
    Multiply both sides by the Least Common Denominator (LCD) to eliminate fractions.
  • What is the Least Common Denominator (LCD) used for in linear equations?
    To clear fractions by multiplying all terms to create an equation without fractions.
  • What are the six steps to solve linear equations with fractions?
    1) Multiply by LCD, 2) Distribute constants, 3) Combine like terms, 4) Group x and constants, 5) Isolate x, 6) Check solution.
  • What are the three possible categories of linear equations based on their solutions?
    Equations can have one solution, no solution, or infinitely many solutions.
  • How can solutions of linear equations be expressed?
    Solutions may be written as a number, no solution, or all real numbers.
  • What is the solution to the equation \(2(x-3)=0\)?
    Solve by distributing: \(2x-6=0\), then isolate x: \(x=3\).
  • 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.
  • What is the purpose of distributing constants in an equation?
    To eliminate parentheses by multiplying the constant across terms inside.
  • What should you do if the equation has variables on both sides?
    Group all variable terms on one side and constants on the other.
  • How do you check your solution to a linear equation?
    Substitute the solution back into the original equation to verify equality.
  • What is the general form of a linear equation in one variable?
    \(ax + b = 0\), where a and b are constants and a \(\neq\) 0.
  • What is the effect of multiplying both sides of an equation by the LCD?
    It clears all fractions, making the equation easier to solve.
  • Why is it important to combine like terms before isolating x?
    To simplify the equation and make isolating x straightforward.