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How Do You Solve an Inequality with Negative Numbers Using Division?

Solve this inequality for t:
-0.8t < -64

Summary

  1. 't' is a variable
  2. -0.8 times 't' is less than -64
  3. Solve for 't' by dividing both sides by -0.8
  4. The two -0.8's cancel out on the left, leaving just 't'
  5. -64 divided by -0.8 is 80
  6. Since we divided by a negative number, we must flip the inequality sign
  7. Check our answer by plugging in 100, and then 10 for 't'

Notes

    1. We are solving for 't' which means that we want to get 't' by itself and on one side
    2. It's on one side, but we need to divide to get 't' by itself
    3. 't' is a variable
    1. Division is the opposite of multiplication, so we need to divide by -0.8
    1. 't' is a variable
    2. Divide the left side by -0.8
    3. The two -0.8's cancel out
    4. 't' is now by itself on the left
    5. The right hand side is -64 divided by -0.8, which is positive 80
    1. Sets are written inside braces, so you can open one with a '{' and close one with a '}'
    1. We can close our set by writing a curly bracket opening to the left, }
    1. 't' is a variable
    2. Pick different values for 't' that represent the different possible answers for 't', and see which ones form a true statement
    1. Any value for 't' greater than 80 should give us a true statement when plugged into our inequality
    2. 't' is a variable
    1. Since our answer is 't' > 80, we should pick something that fits that answer
    2. 't' is a variable
    1. 't' is a variable
    2. We should get a true statement by plugging 100 in for 't'
    3. The left hand side is -0.8 times 100, which is -80
    1. We get a true statement by plugging 100 in for 't'
    2. 't' is a variable
    1. A value for 't' that is less than 80 should produce a false statement when plugged in for 't'
    2. 't' is a variable
    1. A value for 't' that is less than 80 should produce a false statement when plugged in for 't'
    2. 't' is a variable
    1. The left hand side is -0.8 times 10, which is -8
    2. 't' is a variable
    3. We should get a false statement by plugging 10 in for 't'
    1. Negative numbers get greater as they get closer to zero
    2. We get a false statement by plugging 10 in for 't'
    3. 't' is a variable
    1. 't' is a variable
    2. We get a true statement by plugging 100 in for 't'
    3. We get a false statement by plugging 10 in for 't'