Main content

## Algebra 1

### 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)(12 votes)- sir got roasted no idea who is teaching us:))(5 votes)

- I am so confusion, why do they randomly times both sides by -1? They don't even do it in every equation!(3 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.(10 votes)

- Is it just me or does "to calculate the distance they travel on a road trip when they their your average speed and time" make no sense? When I type it in even my computer is trying to correct it. Is this just how you say it in math terms, or did they genuinely make a mistake?(4 votes)
- That's a genuine mistake. Not positive what they were trying to get at, but I think it's simply "to calculate the distance they travel on a road trip based on average speed and time."(6 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(3 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!(3 votes)

- is there a trick to remember them more easily(1 vote)
- 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!(6 votes)

- is there a better way to remember ?(3 votes)
- is there any tricks or ways to remember this more efficiently?(3 votes)
- Anyone know how to do parabolas here.(0 votes)
- What do you mean by "doing parabolas?" These are quadratic equaitons, and you could answer a lot of questions based on these.(6 votes)

- what if it's a word problem? and what if it has to do with averages?(1 vote)
- Help me I don't under stand(1 vote)