# Algebra: Using Mathematical Symbols

## Determining Equations Based on Variables Through the Use of Formulas

Simply put, algebra is about finding the unknown or putting real life variables into equations and then solving them. Unfortunately, many textbooks go straight to the rules, procedures, and formulas, forgetting that these are real life problems being solved and skipping the explanation of algebra at its core: using symbols to represent variables and missing factors in equations and manipulating them in such a way to arrive at a solution.

Algebra is a branch of mathematics that substitutes letters for numbers, and an algebraic equation represents a scale where what is done on one side of the scale is also done to the other side of the scale and the numbers act as constants. Algebra can include real numbers, complex numbers, matrices, vectors, and many more forms of mathematic representation.

The field of algebra can be further broken into basic concepts known as elementary algebra or the more abstract study of numbers and equations known as abstract algebra, where the former is used in most mathematics, science, economics, medicine, and engineering while the latter is mostly used only in advanced mathematics.

## Practical Application of Elementary Algebra

Elementary algebra is taught in all United States schools beginning between the seventh and ninth grades and continuing well into high school and even college. This subject is widely used in many fields including medicine and accounting, but can also be used for everyday problem solving when it comes to unknown variables in mathematical equations.

One such practical use of algebra would be if you were trying to determine how many balloons you started the day with if you sold 37 but still had 13 remaining. The algebraic equation for this problem would be x - 37 = 13 where the number of balloons you started with is represented by x, the unknown we are trying to solve.

The goal in algebra is to find out the unknown and in order to do so in this example, you would manipulate the scale of the equation to isolate x on one side of the scale by adding 37 to both sides, resulting in an equation of x = 50 meaning that you started the day with 50 balloons if you had 13 after selling 37 of them.

## Why Algebra Matters

Even if you don't think you'll need algebra outside of the hallowed halls of your average high school, managing budgets, paying bills, and even determining health care costs and planning for future investments will require a basic understanding of algebra.

Along with developing critical thinking, specifically logic, patterns, problem-solving, deductive and inductive reasoning, understanding the core concepts of algebra can help individuals better handle complex problems involving numbers, especially as they enter the workplace where real life scenarios of unknown variables related to expenses and profits require employees to use algebraic equations to determine the missing factors.

Ultimately, the more a person knows about math, the greater the opportunity for that individual to succeed in the engineering, actuary, physics, programming, or any other tech-related field, and algebra and other higher maths are typically required courses for entrance to most colleges and universities.