If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Algebra 1>Unit 2

Lesson 6: Compound inequalities

# Solving equations & inequalities: FAQ

## 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.

## 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 .

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

## 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)
• sir got roasted no idea who is teaching us:))
• I am so confusion, why do they randomly times both sides by -1? They don't even do it in every equation!
• 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.
• I have a question, why is this so hard
• is there a trick to remember them more easily
• 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!
• 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?
• 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!
• is there a better way to remember ?
• is there any tricks or ways to remember this more efficiently?
• If both of the answers of an And inequality are technically correct, then why do only one of them matter??
• 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.