Equations and Real Life

Mathematics has been taught since preschool and has continued throughout college. In middle school, we learn equations. It is a mathematical statement that is more complex than what we were used to at the younger level. The combination of numbers and letters and sometimes even fractions can be difficult to solve, but somehow, feels rewarding when solved right.

In this article, you will learn all about the basics of equations. Its definition, types, and examples, as well as its application in real life. Lastly, this article will answer the question “Why are equations important?”

What is Equation?

An equation is a mathematical statement that has two equal expressions. It is formed by an expression, followed by an equal sign, and then another expression. The equation is one of the fundamental solutions in more advanced math problems. It helps solve algebra, calculus, and other branches of math. 

Take the equation 2 + 3 = 5 as an example. In this equation, the equal sign appears between 2 + 3 and 5, indicating that both expressions are equal in value, even though they are formed differently. Here, 2 + 3 is an expression that involves addition, while 5 is a single numerical value. This equation asserts that both expressions represent the same quantity.

Elements of Equations

The elements of an equation are: variables, operations, constants, coefficients, terms, exponents, and of course equal signs. These elements can be all included in one equation and sometimes not. However, it depends on the type and difficulty of the problem. Below is the list of elements and how it’s used in an equation.

• Variables – letters that are like x and y. They are representations of unknown values in the expression. In the equation, 2x+3=9, x is the variable. 
• Coefficient – This is the number linked to the variable. In the example above, 2 is the coefficient.
• Terms – A combination of variables, coefficients, or constants, separated by plus or minus signs. Example: In 2x + 3 = 9, the terms are 2x, 3, and 9.
• Operations – The math symbols that tell us what to do with numbers, like + (add), - (subtract), × (multiply), and ÷ (divide). Example: In 2x + 3 = 9, the operation is addition (+).
• Exponent – This is the number that tells how many times to multiply a value by itself. For example, in 4², the number 4 is multiplied by itself two times: 4 x 4
• Constant – A number that doesn’t change, meaning it has no variables attached. Example: In 2x + 3 = 9, the constant is 3.
• Equal Sign – The = symbol, which shows that both sides of the equation are the same in value.

7 Types of Equations: Formula and Examples

The seven types of equations are: Linear, Quadratic, Cubic, Radical, Exponential, Trigonometric, and Rational. To clarify, there are other types of equations but these 7 are the foundation of more complex types. In addition to that, it is broadly categorised into different types based on their structure and the type of solutions they yield.

1. Linear: A linear equation has a variable with an exponent of 1 and no higher powers.
   • Form: ax + b = c
   • Example: 2x + 3 = 7
2. Quadratic: A quadratic equation has a variable raised to the power of 2 (x²).
   • Form: ax² + bx + c = 0
   • Example: x² - 4x + 3 = 0
3. Cubic: A cubic equation has a variable raised to the power of 3 (x³).
   • Form: ax³ + bx² + cx + d = 0
   • Example: x³ - 3x² + 2x = 0
4. Radical: Radical equations have a variable inside a square root (or other roots like cube roots).
   • Form: √(expression) = constant
   • Example: √(x + 3) = 5
5. Exponential: An exponential equation has a variable in the exponent (like x is in 2x).
   • Form: a^x = b
   • Example: 2^x = 16
6. Trigonometric: A trigonometric equation includes trig functions like sine (sin), cosine (cos), and tangent (tan).
   • Example: cos x + 4 = 5
7. Rational: A rational equation has fractions with variables in the denominator. We solve by finding a common denominator or cross-multiplying.
   • Form: (expression) / (expression) = constant
   • Example: (x + 2) / (x - 1) = 3

Real-life application of equations

Equations have been the foundation of mathematical and scientific discoveries. These numerical statements have greatly contributed to human progress in fields such as science, construction, health, and business. Without equations, we might not have advanced into the modern world we live in today. They continue to shape our future, driving innovation and development for a better world.

Here are several areas that heavily rely on equations. The number of areas using these makes it advantageous for anyone to be engaged in.

Problem-Solving

Equations allow for systematic problem-solving, helping individuals and professionals derive precise answers to complex questions. The simplest example of this is word problems in grade school math. Questions such as, “If I have 3 apples and buy 2 more, how many apples do I have in total?” This problem can be represented by 3 + 2 = x. By solving it, you will have the correct answer of 5.

Scientific Discovery

Equations are fundamental in scientific research, enabling the formulation of laws and theories, such as Einstein’s equation E = mc², which explains the relationship between energy and mass. From here on out, scientific discoveries based on the principles of energy relativity have greatly benefited both the scientific community and humanity.. 

Technological Advancements

The technology relies heavily upon mathematics. It provides the foundation for analysing data, understanding algorithms, and much more. For those reasons, math is used as a language in this field. For instance, AI technology uses the linear regression equation Y = MX + C to be able to predict and answer questions in a human-like manner. 

Business Finance

Equations play a crucial role in finance, including calculating interest rates, loan payments, and investment growth. Just the simple use of subtraction in counting your change is already a great use of it. 

Engineering Applications

Whether in civil, mechanical, or electrical engineering, they are necessary for designing infrastructure, circuits, and machines. One of the basic but most used examples is the Pythagorean theorem. The formula, a² + b² = c², is the basis of solving foundation strength, roof slope, and a lot more. 

Medicine and Pharmacology

Equations help model biological systems, calculate drug dosages, and predict the spread of diseases. Through this, medical professionals such as doctors, pharmacists, and nurses can make proper decisions backed up by accurate computations, helped by mathematics. 

Closure: Why are Equations Important?

Equations are important because they provide clear and structured answers to both simple and complex problems. By balancing two mathematical expressions, people can find the exact value of an unknown variable, making problem-solving more accurate. This fundamental concept has led to significant progress in science, technology, and everyday life. As we continue to explore and apply it, we shape the future and drive further advancements for humanity.

In the College of Contract and Management, we teach more than just equations. We offer other math practices that can help in business, construction, health, and technology. Enrol with us today and gain the skills you need for a successful future.