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1.5 – Solving Literal Equations and Formulas


  • Solve literal equations with two variables.
  • Rearrange formulas to solve for a quantity of interest in a real-world problem.
  • Describe the steps in solving equations.
  • Use units to guide and interpret your solutions of literal equations and formulas.


Key Terms

  • Formula – an equation that describes an important mathematical relationship.
  • Literal Equation – an equation that involves two or more variables.



  • If you have two variables, you can solve for either one of them using reverse operations, even without having a value to substitute
    • Example:  Fahrenheit and Celsius are ways to tell the temperature.  In the USA, we use Fahrenheit.  In Europe, they use Celsius.
    • Here is the formula for finding Celsius:
      • C=\frac{5}{9}(F-32)
    • What if you wanted to solve for Fahrenheit instead?  Try solving for F by doing inverse (reverse) operations until you isolate the F.
      • Step 1: Multiply by 9 on both sides
        • 9C=9*\frac{5}{9}(F-32) and this will give you:  9C=5(F-32)
      • Step 2: Divide by 5 on both sides
        • \frac{9}{5}C=5\frac{(F-32)}{5} and this will give you: \frac{9}{5}C=F-32
      • Step 3: Add 32 to both sides
        • You get the formula for finding Fahrenheit:  \frac{9}{5}C+32=F
        • If you want, you can rewrite it as F=\frac{9}{5}C+32


  • Example: Substitution
    • Find x when y = 6 in the literal equation 5x + 4y = 39
    • Step 1: Write with substitution: 5x + 4(6) = 39
    • Step 2: Simplify: 5x + 24 = 39
    • Step 3: Isolate the variable by subtracting 24 from both sides, THEN by dividing by 5 on both sides.
    • Answer: x = 3


  • Example: Inequality setup
    • Question: Maya is taking her friends to a concert. Each ticket costs $25, and souvenir T-shirts are $12 each. There is a $4 service fee for the entire purchase. She has $130. If she buys 3 tickets, how many T-shirts can she buy?
    • Given:  x = number of tickets and y = number of T-shirts.  Set up the inequality.
      • Take notes on what you have:  Tickets: $25, T-Shirts: $12, Service Fee (one time) $4, Total Budget $130
      • Answer:  25x + 12y + 4 ≤ 130


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