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## College Algebra

### Unit 1: Lesson 4

Compound inequalities

# Compound inequalities: AND

Sal solves the compound inequality 3y+7<2y AND 4y+8>-48. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• how is 3y - 2y just y at :42 of the video?
• because 3y-2y equal to 1y, which is the same as just "y".
• If we got that y < -7; and y > -14, is it correct to state it like this: -14 < y < -7 ??
• Yes, that is the most common way of expressing that type of solution. You could also just leave it as an "and" statement as you did in the first half of your comment, or even put it in set and interval notation. They all mean the same thing, and it just comes down to the visual representation that you click with the best (or that your teacher or test requests).
• what is the difference between compound inequalities one and two
• The first equation he did in "Compound Inequalities 1 video" had a "or" in between the two inequalities while this video has a "and" in it.

"Or" means it can satisfy either one of the inequalities or both while "and" means it has to satisfy both inequalities for x to qualify. You can do this by inserting a number that falls in the number line that you made for x, or after finding "x" inserting one of the numbers that x could be.
• I am very confused. How do you answer the questions? I already know how to break down an inequality to x<7 from 3x+4>25 or something like that, but if it gives me a question like:
2x+3≥7 OR 2x+9>11
Where inequality 1 breaks down to x≥2 and in equality 2 breaks down to x>1, how would the answer be
x>1? I don't get it, because couldn't the answer very well be x≥2 because it says OR?? I am very confused. Please help me.
• This is a very good question! In a problem where it says OR, either of the equalities or both equalities can satisfy the equation. In this instance, x>1, when graphed on a number line, and since the equality is greater than 1, x>1 definitely satisfies both equalities because its line encompasses the other equality's line. I would encourage you to make a number line and graph the two equalities to visualize them. This may help to alleviate your confusion.
• what happens when you divide a negative by a negative and isolate it?
By the way, N means negative and P is positive.

N*P=N
P*N=N
N*N=P
P*P=P

ta da!
• Wait, how are AND inequalities different from OR inequalities?
• Let me explain with an example. Let's take two inequalities
x<3, x>1
If the two inequalities are joined by AND, both of the inequalities must be satisfied by the values of x. In other words, both the inequalities must be true at the same time.
x<3 AND x>1 means x must be smaller than 3 and x must be larger than 1. Clearly x must lie between 1 and 3 so x∈(1,3).
If the two inequalities are joined by OR, the inequality will be true even if the value of x is true for one inequality and false for the other inequality.
x<3 OR x>1 means that x is less than 3 or x is greater than 1. Since any one of these possibilities is true for every real number, x∈R.
In essence, when using AND to join 2 inequalities we take the intersection of the solution sets of the 2 inequalities and when using OR to join 2 inequalities we take the union of the solution sets of the 2 inequalities.
• How can you tell if all values of x can be solutions in the exercise after this video?
• You can put the values of x into the inequality as a solution and work it out. If the remaining(or simplified) part of the equation is correct, then that solution out of the number of solutions you got for x in the inequality is correct.
• So in the practice problems, how come when it is the intersection of two points, and the arrows are pointing left, you take the lesser of the two points? Wouldn't it make more sense to take the larger if the arrows are pointing left
• The word "and" tells you to find the intersection of the 2 solutions sets. An intersection is where the 2 sets overlap (or the values they have in common). The "and" is basically telling you that the numbers in the final solution set need to work in both inequalities.

If you take the larger of the 2 arrows, then you are finding the union of the 2 solution sets. If the compound inequality used the word "or", then it means you need the union. The numbers in the union set need to work in only one of the 2 inequalities.

Hope this helps.