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### Course: Integrated math 1>Unit 2

Lesson 6: Compound inequalities

# Compound inequalities examples

Sal solves several compound linear inequalities. Created by Sal Khan and CK-12 Foundation.

## Want to join the conversation?

• When and where to use brackets like ( ) and [ ].

Thanks!
• The brackets and parenthesis are used when answering in interval notation.

( means < or > It is the same as an open dot on the number line.
[ means <= or >= It is the same as a closed dot on the number line.
• at , Sal uncle says, "the less than sign changes to a greater than sign", how is that possible?
• Hi,
When dealing with inequalities, anytime we multiply or divide by a negative number, we have to flip the sign. The reason for that is fairly simple:
Let's say we have the inequality
10 < 25
If we multiply or divide by a positive number, the inequality still holds true
10(2) < 25(2)
20 < 50
However, if we multiply or divide by a negative number we run into a problem
10(-3) < 25(-3)
-30 < -75
As we can see, -30 is not less than -75. -75 is less than -30 (look at a number line if you aren't sure about this). So to keep this inequality correct, since we multiplied by a negative number, we have to flip the sign:
-30 > -75
It doesn't matter if we have constants or variables in our expressions, in all cases, if we multiply or divide by a negative number, we have to flip the sign.
Hope that helps :-)
• At , Is there some way to write both results as an interval? Or should it be separately?

(-∞, 2/3); [2, ∞)
• You would use 'U', which means union.
(-∞, 2/3) U [2, ∞)
• I understand how he solves these but I don't understand how to know if we are supposed to use AND or OR. Please explain the AND, OR part of the compound inequalities.
• You use AND if both conditions of the inequality have to be satisfied, and OR if only one or the other needs to be satisfied.
• What happens if you have a situation where x is greater than or equal to zero and x is greater than or equal to 6? I put no solution on a test because it doesn't make sense that x could be equal to 6 and 0....
• Lets look at them individually:
x >= 0, what is x? x can be 0,1,2,3,4,5,6,7,8,9,10...infinity
x >= 6, what is x? x can be 6,7,8,9,10....infinity
Now what does It want,? It says AND. And means that you need the area where the statement is true for both parts.
What parts are true for both? Well 3 isn't because although it works for the first, it does not work for x>=6, so not 3. How about 6? 6 > 0, so yes there, and 6=6 so yes to the second. So 6 is good. Now how about 10? 10>0 so yes, and 10>6 so yes.
Therefore, you can keep testing points, but the answer is:
x>=6
• I was solving this problem:
Solve for a:
−9a≥36 or −8a>40

and got the answer a≤−4 or a<−5

but the site says the correct answer is a≤−4

Could someone explain this to me? Thanks
• You have the correct math, but notice that this is an OR problem. when a < -5 it is covered by a≤−4. Thus, a<-5 is redundant and need not be mentioned.

If this problem had been −9a≥36 AND −8a>40, then the answer would have been a <-5 because when -5<a≤−4 it does not satisfy a<-5.

So, for an AND problem you specify the intervals that satisfy both conditions. For an OR problem, you need to specify the intervals that satisfy either of the conditions.
• Hi
thank you for your beautiful videos
I do not undertsand how, in the second inequality solved in this video, 14/5 becomes 2.4/5....
Nicola
• at , when sal does the inverse operation of 9/2, why does he use 2/9 instead of 9/2?
• Sal used 2/9 because he was trying to isolate the 'x' variable.

2/9 x 9/2 is basically 18/18 which is 1.
so 2/9 x 2/9 X is 1X which is X

If Sal used 9/2
it would be 9/2 x 9/2X which would be 81/4X.

Hope this helps!