Do Algebraic equations worry you like many other students? Don’t worry. You have come to the right article. In this article, you will be introduced to the definitions, their types, and how to solve algebraic equations simply and easily. Let’s start this topic.
What is an Equation?
The word equation comes from the word equal. In simple words, an equation is formed when two expressions are equal.
For example,
3 + 5 – 2 = 6
What is an Algebraic Equation?
An algebraic equation is an equation in which two algebraic expressions are equal.
For example,
2x + 5 = 4
Note:
Every simple algebraic equation is an equation, but not every equation is algebraic. If you want to understand algebraic expressions in more detail, you should first visit the article on algebraic expressions.
Difference between an Equation and an Algebraic Equation:
Here is an algebraic equation worksheet that will help you to understand the main difference between an Equation and Algebraic Equations.
Equations vs Algebraic Equations
| Characteristics | Equation | Algebraic Equation |
| Equal sign | yes | yes |
| Variables | May or may not be | yes |
| Examples | 2 + 3 = 5 | 2x + 3 = 5 |
| Purpose | For showing Equality | For finding unknown values |
| Nature | Arithmetic or Algebraic | Only Algebraic |
Types of Algebraic Equations
There are many types of algebraic equations. As we know, these equations involve variables. So all kinds will be based on the degrees of the variables. In this section, we will understand each heading with relevant examples.
1. Linear Algebraic Equations:
An equation in which the degree of the variable is 1 is known as a linear equation.
General form:
y = mx + b
For example
2x + 4 = 6
2. Quadratic Algebraic Equations:
Equations with degree 2 of the variables are called quadratic equations.
General form:
ax2+ bx + c = 0
For example
2x^2 + 4 = 6
3. Cubic Algebraic Equations:
These are the equations whose variables have degree 3.
General form:
ax^3 + bx^2 + cx + d = 0
For example
2x^3 + 4 = 6
4. Polynomial Algebraic Equations:
The word “Poly” is a Greek word that means “many”, and the word “nomial” means “terms”. Therefore, an Equation in which more than one term is used is called a polynomial Equation.
General form:
P(x)=anxn+a{n-1}x{n-1}+. . . . . +a1x+a0=0
For Example
2x^3 + 4x^2 + 3x + 6 = 0
Note:
In all these types, x is used as a variable, n is used as the degree, and a, b, and c are used as coefficients. The term “degree” used means the highest power of the variable present in an equation.
How to Solve Algebraic Equations like a Pro
Feeling stressed about solving problems?
Relax, here you will be shown the puzzle pieces step by step so that you can solve algebraic problems.
Let’s start with the basic rules and the step-by-step method of simplifying algebraic equations.
1. Keep the balance:
Keep in mind balancing algebraic equations like a weighing machine. This means that the steps you take on one side of the equation should be taken on the other side.
For example:
2x + 6 = x + 9
2. Collect the same terms:
Place the variables on one side and the numbers on the other side.
2x – x = 9 – 6
3. Simplify:
Solve the equation according to the BODMAS rule so that it is converted to its simplest form.
x = 3
4. Get your answer:
Finally, you have found the value of the variable.
x = 3
5. Checking:
Plug your x back into the original equation to make sure it works.
2x + 6 = x + 9
2 (3) + 6 = 3 + 9
6 + 6 = 3 + 9
12 = 12
Solving Algebraic Equations Examples:
Here are some examples.
- Linear Algebraic Equations
Solve 5x + 5 = 3x – 5
Solution:
Put the variables on one side and the constants on the other side.
5x – 3x = – 5 – 5
Simplify
2x = – 10
x = -10∕2
Answer
x = -5
- How to Solve Algebraic Equations with Fractions
Solve
x ∕ 3 + 3 = 1
Solution:
Put the constants on the other side.
x ∕ 3 = 1 − 3
Simplify
x ∕ 3 = -2
Multiply both sides by 3
x = -6
Answer
x = -6
- Algebra Equations with Brackets
Solve
2(x + 5) = 16
Solution:
Open the brackets.
2x + 10 = 16
Put the constant on the other side.
2x = 16 − 10
Simplify
2x = 6
x = 6 ∕ 2
Answer
x = 3
Quadratic Algebraic Equation
Solve
x² − 25 = 0
Solution:
Put the constant on the other side.
x² = 25
Take the square root of both sides.
x = ±5
Answer
x = 5 or x = −5
Algebraic Equations with Square Roots
Solve
√x − 2 = 0
Solution:
Put the constant on the other side.
√x = 2
Square both sides.
x = 4
Answer
x = 4
Mistakes while Solving the Problems:
- Keeping the equation unbalanced:
Often, students make a step that makes the equation unbalanced.
- Forgetting to combine like terms:
Sometimes, they start solving a question without combining like terms.
- Ignoring signs:
This is the most common mistake students make. Simplification often leads to confusion with signs.
- Skipping steps:
Skipping steps compromises your solving method. Each step should be solved sequentially.
- Not checking the final answer:
This step alone makes it clear whether your answer is correct or wrong.
FAQs
Q1. What is an algebraic equation?
Answer. An equation that contains terms of algebra is called an algebraic equation.
Q2. What is the purpose of algebraic equations?
Answer. These equations are helpful in both academic and daily life.
Q3. How to solve algebraic equations step by step?
Answer. If you follow all the above steps to solve equations, it will be easier for you.
Q4. Are all algebraic equations equations?
Answer. Yes, all algebraic equations are equations, but not all equations are algebraic.
Q5. What are the types of algebraic equations?
Answer.
- Linear equations
- Quadratic equations
- Cubic equations
- Polynomial equations
Conclusion:
“This article tries to provide all the information about algebraic equations, starting from their introduction to their types, examples, and related concepts. Based on this article, one can gain complete command over the algebraic equations.”
