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### Course: Algebra 1 > Unit 2

Lesson 6: Compound inequalities# Solving equations & inequalities: FAQ

Frequently asked questions about solving equations & inequalities

## Why do we need to learn about linear equations?

Linear equations are a fundamental part of algebra, and they're often used to model real-world situations. For example, someone might use a linear equation to figure out how much money they will have left after spending a certain amount each week, or to calculate the distance they travel on a road trip when they know their average speed and time.

## What does it mean to have variables on "both sides" of an equation?

This refers to a linear equation where we have a letter on both sides of the equals sign. For example, $3x+4=2x+7$ has variables on both sides, but $3x+4=10$ does not.

Practice with our Equations with variables on both sides
exercise.

## What's the difference between a multi-step inequality and a compound inequality?

A multi-step inequality has more than one operation in it, for example $2x-5>7$ . A compound inequality is the combination of two inequalities, for example $x>3\text{AND}x7$ .

Practice with our Multi-step linear inequalities
exercise.

Practice with our Compound inequalities
exercise.

## How do we figure out the number of solutions to a linear equation?

One way to figure out how many solutions there are to a linear equation is to try to isolate the variable on one side of the equation.

- For an equation with one solution, consider the equation
. If we isolate the variable, we find that$2x+3=11$ .$x=4$ - For an equation with no solution, consider the equation
. If we try to isolate the variable, we end up with a false statement like$2x+3=2x+7$ when we subtract$3=7$ from both sides of the equation. Since$2x$ does not equal$3$ , there is no solution to this equation.$7$ - For an equation with infinite solutions, consider the equation
. If we try to isolate the variable, we end up with a statement that is always true like$2x+3=2x+3$ when we subtract$3=3$ from both sides of the equation. Since 0 = 0 is always true, any value of$2x$ will satisfy the original equation. So there are infinite solutions.$x$

Practice with our Number of solutions to equations
exercise.

## Want to join the conversation?

- or to calculate the distance they travel on a road trip when they their your average speed and time.

You need an editor! haha That is not a sentenee (or a phrase)(17 votes)- sir got roasted no idea who is teaching us:))(10 votes)

- I am so confusion, why do they randomly times both sides by -1? They don't even do it in every equation!(5 votes)
- Usually you do that in order to change the "x" into positive, because it's usually easier to think in that way, for example. -x = 2c + 5; after multiplying all by -1: x = -2c - 5. It's very simple as well, just invert the "+" and "-" signs in the whole equation. So, the multiplication by -1 is not random, usually it happens when x (or any other variable) has a negative value. I hope this is what you were asking, and I hope I helped. Keep at it.(15 votes)

- I have a question, why is this so hard(11 votes)
- is there a trick to remember them more easily(0 votes)
- U could make it easy on urself and write on a peace of paper how an infinity etc. looks like so if u do the equation u can see by the answer that it is infinity solutions, non solutions or only 1 solutions, like

1 solution = (X=5)

no solutions = (4=7)

infinite solutions = (5=5)

hope this helps, have a great day!(12 votes)

- Compound inequality is defined here as a combination of
**two**inequalities. Is it really just limited to only**two inequalities**or can it be a combination of?**more than two**inequalities(4 votes)- yes it could but then you are going to get 3 answers and its going to look confusing if u draw it on a number line like (x<23, x>4, x<-1) hope this helps, have a great day!(4 votes)

- is there a better way to remember ?(4 votes)
- is there any tricks or ways to remember this more efficiently?(4 votes)
- If both of the answers of an And inequality are technically correct, then why do only one of them matter??(2 votes)
- Both matter. AND means both inequalities are true.

x > 10 AND x > 15

The result is x > 15 because only in the region x > 15**both x > 10 AND x > 15**are true.

x ≤ -5 AND x < 0

The result is x ≤ -5 because only in the region x ≤ 5**both x ≤ 5 AND x < 0**are true.

I suppose these 2 inequalities are the type that gives you a false believe that only one of them matter, but actually both matters.

x ≤ -5 AND x ≥ 0

The result is 0 ≤ x ≤ -5. This should be obvious that not only one of them matter.(3 votes)

- rememder when we thought regular math was hard now thats so easy and this is hard sooner or later we r gonna think this is easy (maybe)(3 votes)
- What's the difference between compound inequalities and double inequalities? Are they the same thing?(2 votes)
- Compound inequalities and double inequalities are closely related concepts in mathematics, dealing with ranges of values for a variable. Compound inequalities involve two separate inequalities combined into one statement using "and" or "or," indicating that either both conditions must be true simultaneously or at least one condition must be true. On the other hand, double inequalities specifically describe situations where a single variable is constrained between two values using "and" implicitly, expressing a range within which the variable must lie. Essentially, double inequalities are basically a subset of compound inequalities, that focus on defining a variable's limits within a specified range.(2 votes)