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How Do You Solve an Inequality with Negative Numbers Using Division?
Solve this inequality for t:
-0.8t < -64
Summary
- 't' is a variable
- -0.8 times 't' is less than -64
- Solve for 't' by dividing both sides by -0.8
- The two -0.8's cancel out on the left, leaving just 't'
- -64 divided by -0.8 is 80
- Since we divided by a negative number, we must flip the inequality sign
- Check our answer by plugging in 100, and then 10 for 't'

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