Types of Solutions: Linear 1-Variable Equations

Have you ever noticed in track and field that short distance runners get to run in their own lane, but the long-distance runners eventually share the same lanes?

Standard(s) Supported: 8.EE.C.7.A

What is a linear 1-variable equation?

First, why the word ‘linear’? To make sure we are only looking at equations where the variable has an exponent of 1. When a variable appears to have no exponent, like x, it really has an exponent of 1.

What is a linear 1.pdf

To learn more about the different types of equations you will study in math, check out the fundamental Types of Equations!

**check back soon - still in the works**

What are the different types of solutions to a linear 1-variable equation?

What are the different types of solutions to a linear 1.pdf

How do you solve a linear 1-variable equation that has one solution, infinite solutions or no solution?

Example 1: ONE solution

Example 1.pdf

Example 2: INFINITE solutions

Example 2.pdf

Example 3: NO solution

Example 3.pdf

If you need more help with isolating the variable using inverse operations to solve 1-variable equations check out the fundamentals: Solving 1-Variable Equations: Variable on One Side of the Equation; and Solving 1-Variable Equations: Variable on Both Sides of the Equation!

If you need more help with combining like terms and the distributive property while solving 1-variable equations, check out the fundamental: Solving Complex 1-Variable Equations!

Why do we learn about the different types of solutions to linear 1-variable equations?

Let’s think of the path of two planes and assume they are flying in a straight line. You could write an expression that represents their distance above the ground and determine if the planes are either a) on paths that will eventually cross (one solution) b) on the same path (infinite solutions) or c) on paths that will never cross (no solution). This same concept could be applied to a business model that is trying to figure out when their company will break even on production costs of a new product. If production costs continue at the same rate as earnings, then no solution would be found. Obviously, a company would hopefully have figured this out before production. Case in point, mathematics is the language used to explain the world in which we live. All mathematics was developed at some time in our past to model a situation and from these models we can now explain new and different situations.

What’s next? When you separate an equation into its two expressions and graph each expression individually, you get a system of equations. Check back soon for more on…Systems of Equations!