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Linear Equations quiz #1 Flashcards

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Linear Equations quiz #1
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  • How do you solve the linear equation 6(x – 1) = 9(x + 2) for x?
    First, distribute both sides: 6x – 6 = 9x + 18. Next, move all x terms to one side and constants to the other: 6x – 9x = 18 + 6, which gives –3x = 24. Finally, divide both sides by –3 to isolate x: x = –8.
  • What are the steps to solve the linear equation 9(x + 1) = 25 + x for x?
    Distribute: 9x + 9 = 25 + x. Move x terms to one side: 9x – x = 25 – 9, resulting in 8x = 16. Divide both sides by 8: x = 2.
  • How do you solve the equation 8x – 2 – 5x = 8 for x?
    Combine like terms: (8x – 5x) – 2 = 8, which simplifies to 3x – 2 = 8. Add 2 to both sides: 3x = 10. Divide both sides by 3: x = 10/3.
  • What is the solution for x in the equation 5(x – 10) = 30 – 15x?
    Distribute: 5x – 50 = 30 – 15x. Move x terms to one side: 5x + 15x = 30 + 50, giving 20x = 80. Divide both sides by 20: x = 4.
  • How do you solve for x in the equation –2x + 4.4 = 23.8?
    Subtract 4.4 from both sides: –2x = 23.8 – 4.4, which is –2x = 19.4. Divide both sides by –2: x = 19.4 / (–2) = –9.7.
  • What general steps should you follow to solve a linear equation for x?
    1. Distribute any constants if needed. 2. Combine like terms. 3. Move all x terms to one side and constants to the other. 4. Isolate x by performing the opposite operation (addition/subtraction/multiplication/division) on both sides. 5. Check your solution by substituting x back into the original equation.
  • What is the first step when solving a linear equation that contains fractions?
    Multiply both sides of the equation by the least common denominator to eliminate all fractions. This simplifies the equation and makes it easier to solve.
  • How do you check if your solution to a linear equation is correct?
    Substitute the value you found for x back into the original equation. If both sides of the equation are equal, your solution is correct.
  • What does it mean if solving a linear equation results in a statement like 0 = 0?
    It means the equation is true for all values of x, so there are infinite solutions. This type of equation is called an identity equation.
  • How is the solution set for a linear equation with no solutions written in set notation?
    The solution set is written as curly brackets containing a zero with a slash through it, representing the empty set. This indicates that there is no value of x that satisfies the equation.