Problem Solving: Writing 1-Variable Inequalities

A 1-variable inequality is an inequality that has only 1 specific variable in the inequality, such as x. The specific variable may occur multiple times in the inequality (2x + 4 – 3x < 7x) and the specific variable may be within non-like terms (5x vs. 2x²). No matter what, to make a 1-variable inequality, only the same variable will be present throughout the inequality.

There are many strategies used for problem solving. Overall, once you hit pre-algebra the key focus in problem solving includes:

1) Identify what you know (are given) in the problem

2) Identify what is unknown (typically the part of the problem in the question)

3) Define your variable(s) (choose a variable to represent the unknown(s))

4) Create a model (could be writing an equation, creating a graph, making a table)

5) Solve your model to calculate the unknown(s)

6) Check your work

Let’s face it, problem solving is not easy and remembering all the above steps when you are first starting out can seem like a lot. So, this site is going to focus on the strategy that uses the acronym CUBES. If you have used CUBES before in math, you may notice that the below CUBES chart looks a little different than it did in the early years of math. Why? Because as you progress through math and learn more, your techniques and strategies need to grow right along with you.

CUBES – general method to help problem solve and write equations

Example 1: using CUBES and writing 1-variable inequalities

Example 2: using CUBES and writing 1-variable inequalities