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1.1 Linear Equations

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1.1 Linear Equations. A linear equation in one variable is equivalent to an ... Examples of equivalent equations: Solving a Linear Equation. Solve the equation: ... – PowerPoint PPT presentation

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Title: 1.1 Linear Equations


1
1.1 Linear Equations
  • A linear equation in one variable is equivalent
    to an equation of the form
  • To solve an equation means to find all the
    solutions of the equation.

2
Equivalent Equations
  • Two or more equations that have precisely the
    same solutions are called equivalent equations.
  • Examples of equivalent equations

3
Solving a Linear Equation
  • Solve the equation
  • We replace the original equation by succession of
    equivalent equations.
  • Add 5 to both sides.
  • Simplify.
  • Divide both sides by 3.
  • Simplify.

4
Solving a Linear Equation Involving Fractions
  • Multiply both sides by the least common
    denominator 30.
  • Be sure to multiply all terms by 30.
  • Divide out common factors.
  • Subtract 5x to get the x-terms on the left.
  • Simplify.
  • Solve the equation

5
Solve an Equation Involving Rational Expressions
  • Solve

6
This is the given equation. Multiply both sides by 5x (LCD). Be sure to multiply all terms by 5x. Divide out the common factors. Simplify. Subtract 4 from both sides. Divide both sides by 2.
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