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How Do You Use Division with Negative Numbers to Solve an Inequality Word Problem?

After 18 holes of golf Marie has a score of -3. The record at this golf course is -12. What factor does her score have to improve by in order for her to beat the record?

Summary

  1. Marie's current score is -3 and multiply that by 'n' to beat the record of -12
  2. '<' means less than
  3. Divide both sides by 3
  4. We get 'n' on the left, and 4 on the right, and we flip the inequality symbol
  5. '>' means greater than

Notes

    1. 'n' is a variable representing the multiplier that Marie must improve her score by
    1. This is what we are trying to figure out
    2. Her score is -3
    3. 'n' is a variable representing the multiplier that Marie must improve her score by
    1. Marie needs to improve her score by 'n' times
    2. 'n' is a variable representing the multiplier that Marie must improve her score by
    1. To beat the old high score in golf, Marie's new score of '3•n' needs to be less than -12
    2. 'n' is a variable representing the multiplier that Marie must improve her score by
    1. Division is the opposite of multiplication
    2. So to cancel out the multiplication, we divide by -3
    1. We're dividing both sides by -3
    2. The -3's cancel out on the left side leaving just 'n'
    3. -12 divided by -3 is a positive 4 on the right
    1. We divided by -3, so the < sign becomes a > sign
    1. So Marie has to do 5 times as well as she does right now