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## Algebra 1

### Course: Algebra 1>Unit 2

Lesson 6: 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?

• 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!
• where did -10 come from?
• It's just a random number he chose that was between -14 and -7.
• I'm having a lot of trouble with the exercise after this. I don't have a problem with solving the inequalities themselves, but I don't understand the part when it asks if there's no answer, or if all values of x are answers, or if x is more than/less than y, etc. Can someone help me?
• I don't understand where you got those numbers for the number line I am very confused do I need that or was it just to help in something?
• To solve a compound inequality, you start by solving each individual inequality. Then, the word "AND" or "OR" tells you the next step to take.

AND tells you to find the intersection of the two solution sets. An intersection is the values in common or the overlap of the two sets. This is why it is common to graph the 2 original inequalities. From the graph, you can quickly identify what values are in common because it is where the graphs overlap.

OR tells you to find the union of the two solution sets. A union combines all solutions from the original inequalities into one solution set. If a value works for either inequality or both inequalities, it goes in the union.

Hope this helps.
• 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.