Single variable equations are some of the most common types of problems on the ACT math section. You must know how to set up, use, and manipulate these kinds of equations, as they are a foundational element of mathematics upon which more complicated expressions (multiple variable, quadratics, etc.) are based.
So make sure you are prepared to tackle the ins and outs of single variable equations (no matter how they are presented on the ACT), before you take on some of the more complicated elements of ACT math.
This guide will be your complete walk-through of single variable equations for the ACT–what they are, how you’ll see them on the test, and how to set up and solve them.
And the mystery unfolds.
What Are Single Variable Equations?
To understand a single variable equation, let us break it into its two components: the variable and the equation.
A variable is a symbolic placeholder for a number we do not yet know. It’s very common to see x or y used as a variable in math problems, but variables can be represented by any symbol or letter.
x+4=14
In this case, x is our variable. It represents a number that is currently unknown.
An equation sets two mathematical expressions equal to one another. This equality is represented with an equals sign (=) and each side of the expression can be as simple as a single integer or as complex as an expression with multiple variables, exponents, or anything else.
| (x+y2) |
| 14 |
−65(x−3)=2
The above is an example of an equation. Each side of the expression equals the other.
So if we put together our definitions, we know that:
A single variable equation is an equation in which there is only one variable used. (Note: the variable can be used multiple times and/or used on either side of the equation; all that matters is that the variable remains the same.)
| (x+4) |
| 2 |
=12
6x+3−2x=19
4y−2=y+7
These are all examples of single variable equations. You can see how some expressions used the variable multiple times or used the variable in both expressions (on either side of the equals sign).
No matter how many times the variable is used, these still count as single variable problems because the variable remains constant and there are no other variables.
Finding your missing variable is like finding that last missing piece of the puzzle.
