"How to Solve a Linear Equation in one Variable"

 

A linear equation with one variable is an algebraic expression that can be written in the form ax + b = c, where a, b and c are constants and x is the unknown variable. To solve a linear equation with one variable, we need to isolate x on one side of the equation and find its value. Here are the steps involved in solving a linear equation with one variable:

 

1. Simplify both sides of the equation by combining like terms. Like terms are terms that have the same variable and exponent. For example, 2x and -5x are like terms, but x and x² are not.

2. Use the addition or subtraction property of equality to move all the terms with x to one side of the equation and all the constants to the other side. The addition or subtraction property of equality states that if we add or subtract the same number to both sides of an equation, the equation remains true. For example, if we have 2x + 3 = 7, we can subtract 3 from both sides to get

2x +3 -3= 7-3

  2x=4.

3. Use the multiplication or division property of equality to divide both sides of the equation by the coefficient of x. The coefficient of x is the number that is multiplied by x. The multiplication or division property of equality states that if we multiply or divide both sides of an equation by the same nonzero number, the equation remains true. For example, if we have 2x = 4, we can divide both sides by 2 to get

2 x = 4.

2x/2 = 4/2

X = 2

4. Check your solution by substituting it back into the original equation and simplifying. If both sides of the equation are equal, then your solution is correct. Otherwise it is not.

Solve Linear Equation

Let's look at an example of how to solve a linear equation with one variable using these steps:

Solve for x: 3x - 5 = 10

Step 1: Simplify both sides of the equation by combining like terms. In this case, there are no like terms on either side, so we can skip this step.

Step 2: Use the addition or subtraction property of equality to move all the terms with x to one side of the equation and all the constants to the other side. In this case, we can add 5 to both sides to get rid of the -5 on the left side.

 

3x - 5 + 5 = 10 + 5

3x = 15

 

Step 3: Use the multiplication or division property of equality to divide both sides of the equation by the coefficient of x. In this case, we can divide both sides by 3 to get rid of the 3 on the left side.

 

(3x)/3 = 15/3

x = 5

 

Step 4: Check your solution by substituting it back into the original equation and simplifying. If both sides of the equation are equal, then your solution is correct.

 

3x - 5 = 10

3(5) - 5 = 10

15 - 5 = 10

10 = 10

 

Since both sides of the equation are equal, our solution is correct. Therefore, x = 5 is the solution to the linear equation with one variable.

Exercise

Solve the following linear equations in one variable

i)                  6x-2=10

ii)               2x+10=2

iii)            -4x-3=-5

 In the next article, we will be solving linear equations  one variable involving fractions.

This article was written by Awah Aweh who is an expert in writing articles on self-Improvement for the internet at my website's blog here. He is experienced mathematics teacher from 1997 till date.