www.VirtualNerd.com

How Do You Write an Absolute Value Inequality from a Word Problem?

Wanita played outside today and asked her mother if she could play outside tomorrow. Her mother said she could play outside only if the difference between today’s temperature and 80% of tomorrow's temperature is less than 10 degrees. If today’s temperature was 74 degrees, write an inequality for the range of tomorrow’s temperature needed for Wanita to be able to play outside.

Summary

  1. Let 't' represent the range of tomorrow's temperatures
  2. We're looking at a difference in temperatures, so this will be an absolute value inequality
  3. The two vertical bars represent an absolute value
  4. 0.8 is the decimal form of 80%
  5. '<' means LESS THAN

Notes

    1. We're choosing 't' as our variable to represent tomorrow's range of temperatures
    1. A range means we'll have more than one inequality sign, so it can't be a simple inequality
    1. The difference between today's and tomorrow's temperature must be less than 10 degrees
    1. So it doesn't matter if tomorrow is colder or warmer than today, the difference just has to be less than 10 degrees
    1. So it doesn't matter if tomorrow is colder or warmer than today, the difference just has to be less than 10 degrees
    1. Since we just care about the difference, or range, in temperature, we know this is an absolute value problem
    1. Absolute value symbols look like this: | |
    1. Absolute value symbols look like this: | |
    2. The symbols tell us that we only care about the difference itself, not that it's a positive or negative difference
    1. This was given
    1. "Find the difference" here means the same thing as "find the absolute value"
    2. Remember that 't' represents tomorrow's possible temperatures
    1. To convert 80% to a decimal, divide it by 100 and get rid of the % sign
    1. Since 80% is the same as 0.8, we multiply 0.8 by 't'
    2. Remember that 't' is a variable representing tomorrow's possible temperatures
    1. Today's temperature is 74 degrees
    2. So our difference between today and 80% of tomorrow's temperature is '|74-0.8t|'
    3. "The difference" here means the same thing as "the absolute value"
    1. |74-0.8t| < 10
    2. The '<' symbol means LESS THAN
    1. 80% of tomorrow's temperature cannot be 10 degrees warmer or colder than today's temperature
    2. |74-0.8t| < 10
    1. 80% of tomorrow's temperature cannot be 10 degrees warmer or colder than today's temperature
    2. |74-0.8t| < 10
    1. We already combined our parts in Step 3
    1. 80% of tomorrow's temperature cannot be 10 degrees warmer or colder than today's temperature
    2. |74-0.8t| < 10