Linear Equation in One Variable

Linear Equations in One Variable

A linear equation in one variable is an equation that has a maximum of one variable of order 1. It is of the form ax + b = 0, where x is the variable,
a and b are real numbers and both a and b are not equal to zero.

For example, the equation 2x + 3 = 7 is linear with a single variable in it. This can be solved by subtracting 3 from both sides to get 2x = 4 and dividing both sides by 2 to get x = 2.

Degree of Linear Equation in One Variable

The maximum power variable of an equation is known as a degree.
So, the degree of a linear equation is 1.

Therefore, a linear equation is also known as a one-degree equation.

Standard form of Linear Equations in One Variable

The standard form of a linear equation in one variable is: ax + b = 0

where "a" and "b" are real numbers and "x" is the variable. Both a and b are non-zero natural numbers. This form allows for easy comparison and manipulation of equations.

Therefore, the formula of linear equations in one variable is: ax + b = 0

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

1. Simplify the equation as much as possible by combining like terms on both sides of the equation.

2. Use algebraic operations such as addition, subtraction, multiplication, and division to isolate the variable on one side of the equation.

3. Solve for the variable by applying inverse operations to both sides of the equation.

4. Check your answer by plugging it back into the original equation and verifying that both sides of the equation are equal.

For example, solve the equation 4x - 7 = 9.

Solution: Simplify the equation by adding 7 to both sides: 4x = 16

Isolate the variable by dividing both sides by 4:x = 4

Check the answer by plugging it back into the original equation: 4(4) - 7 = 9

16 - 7 = 9

9 = 9

Since both sides of the equation are equal, we can confirm that x = 4 is the correct solution to the equation 4x - 7 = 9.