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## Algebra 1

### 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.