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How Do You Use Addition to Solve an Inequality Word Problem?

Marissa is an impulse buyer and keeps taking money out of her bank account. Looking at her receipts she knows she spent a total of $28.35 so far today. She wants to go to a movie that costs $6.75 but is unsure if she has enough money left in her account. How much money must Marissa have started with in her account in order to afford the movie ticket?

Summary

  1. 'm' is a variable representing the starting money in Marissa's bank account
  2. First subtract the money she spent, $28.35, from 'm'
  3. 'm' minus 28.35 must be greater than or equal to 6.75, the cost of the ticket
  4. '≥' means greater than or equal to
  5. 'm' must be greater than or equal to 35.10 dollars

Notes

    1. 'm' is a variable representing the starting money in Marissa's bank account
    1. Spending $28.35 means that 28.35 should be subtracted
    1. Spending $28.35 means that 28.35 should be subtracted
    2. 'm' is a variable representing the starting money in Marissa's bank account
    1. 'm' minus 28.75 represents the amount of money left in her bank account
    2. 'm' is a variable representing the starting money in Marissa's bank account
    1. The amount in her bank account now, m-28.35, must be greater than or equal to 6.75
    2. 'm' is a variable representing the starting money in Marissa's bank account
    1. Solving for 'm' means that we get 'm' by itself and on one side
    1. The addition property of inequality says that if we add something to one side, we must add it to the other side
    1. 'm' is a variable representing the starting money in Marissa's bank account
    2. Remember we are adding 28.35 to both sides to solve for 'm'
    3. The 28.35's cancel out on the left hand side, leaving just 'm'
    4. The right hand side is 35.10