January 8, 2021

Chapters

In this article, you will learn how to solve linear equations. But before proceeding to that, first, we will see what are the equations.

## Equations

An equation is an algebraic expression that contains an

equalitysign.

It depicts that the left-hand side of the equality is equal to the right-hand side. If you add or subtract the same thing on both sides of the equation, the equation will remain unaffected. There are different types of equations such as linear, exponential, quadratic and logarithmic, etc. In this article, our main focus will be the linear equations only.

An equation of a straight line is known as a linear equation.

For instance, the algebraic expression is a linear equation as it contains "=" sign. It means that x + 9 is equal to 18. So, what is the value of x?

Well, the value of x will be such that both sides are equal. So, it must be 9 because 9 + 9 = 18. In this example, we have only one variable x. That is why it can be known as a linear equation in one variable. We can have an equation containing two or more variables. For instance, consider the following equation:

The above equation has two variables x and y. Hence, we can call it as a linear equation in two variables. It is also given in the slope-intercept form. A slope-intercept form of the linear equation is . Here, m is the slope and b is a constant.

Solving a linear equation in one variable is pretty straightforward. On the other hand, it is not possible to find the value of unknowns in the linear equation in two variables without knowing the value of one variable. To solve the linear equations in two variables, we often have two equations, so we can solve them as a system. Solving a system of linear equations is an entirely distinct concept, therefore in the next section, we will only focus on solving the linear equation in one variable.

## Steps for solving a linear equation in one variable

To solve a linear equation in one variable, follow these steps:

- First, remove the parentheses by solving the terms inside them.
- In the next step, simplify the terms with the denominators.
- Make two groups of the terms, one having the x variable and the other having the constants.
- Apply the arithmetic operations of addition or subtraction to similar terms to reduce them.
- Solve for unknown.

## Example 1

### Solution

## Example 2

### Solution

## Example 3

### Solution

### Step 1 - Remove parentheses

### Step 2 - Remove the denominators

### Step 3 - Group similar terms together

### Step 4 - Add and subtract the similar terms