Skip to main content
Back

College Algebra: Linear Equations Basics minal

Control buttons has been changed to "navigation" mode.
1/13
  • What is a linear equation?
    A linear equation is formed by setting a linear expression equal to a value, such as \(2x+3=5\).
  • What is the goal when solving a linear equation?
    The goal is to find the value of x that satisfies the equation.
  • What operations can be used to solve linear equations?
    Use addition, subtraction, multiplication, and division to isolate x.
  • Why must the same operation be performed on both sides of an equation?
    To maintain equality between both sides of the equation.
  • How do you solve the equation \(x+2=0\)?
    Subtract 2 from both sides to isolate x: \(x=-2\).
  • How do you solve the equation \(3x=12\)?
    Divide both sides by 3 to isolate x: \(x=4\).
  • What is the first step to solve \(2(x-3)=0\)?
    Distribute the 2: \(2x-6=0\).
  • After distributing in \(2x-6=0\), what is the next step?
    Add 6 to both sides: \(2x=6\).
  • How do you find x after isolating terms in \(2x=6\)?
    Divide both sides by 2: \(x=3\).
  • What is the solution or root of an equation?
    The value of x that satisfies the equation.
  • How do you verify a solution to a linear equation?
    Substitute the solution back into the original equation and check if both sides are equal.
  • Verify the solution \(x=3\) for the equation \(2x-3=0\).
    Substitute: \(2(3)-3=0\) simplifies to \(6-3=3\), which equals 3, so the solution is valid.
  • What is the importance of mastering linear equations?
    It lays the groundwork for more advanced mathematical concepts and helps solve various equations effectively.