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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 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.

## 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.

## 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.