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## 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 their your 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, 3, x, plus, 4, equals, 2, x, plus, 7 has variables on both sides, but 3, x, plus, 4, equals, 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 2, x, minus, 5, is greater than, 7. A compound inequality is the combination of two inequalities, for example x, is greater than, 3, start text, space, A, N, D, space, end text, x, is less than, 7.

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 2, x, plus, 3, equals, 11. If we isolate the variable, we find that x, equals, 4.
- For an equation with no solution, consider the equation 2, x, plus, 3, equals, 2, x, plus, 7. If we try to isolate the variable, we end up with a false statement like 3, equals, 7 when we subtract 2, x 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 2, x, plus, 3, equals, 2, x, plus, 3. If we try to isolate the variable, we end up with a statement that is always true like 3, equals, 3 when we subtract 2, x 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.

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)(11 votes)- sir got roasted no idea who is teaching us:))(4 votes)

- I am so confusion, why do they randomly times both sides by -1? They don't even do it in every equation!(4 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.(8 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."(5 votes)

- I think this is a grammatical error: "..or to calculate the distance they travel on a road trip when they their your average speed and time."(6 votes)
- I agree; it is an editorial mistake. Personally, I think shortening the sentence would be better.

One way of rephrasing it could be:

"... 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, or their average speed and time."(0 votes)

- Anyone know how to do parabolas here.(3 votes)
- What do you mean by "doing parabolas?" These are quadratic equaitons, and you could answer a lot of questions based on these.(5 votes)