Solving Equations Involving Simplification

When you study mathematics, equations are a significant part of it. Solving equations involving simplification is another vital topic that mainly includes the concept of addition, subtraction, division, and multiplication. This article talks about solving equations involving simplification. You will find brief information on the concept of equations in Maths, a thorough explanation of solving equations involving simplification, examples of it, and so on.

Explain Equations in Mathematics 

Equations are one of the basics of mathematics which can be defined as an expression that equals two different values. The equations are further separated by an equal sign placed in the middle. In case the equation has the equal sign (=), it means that the value of the left-hand side should be the same as the value on the right-hand side of the equation. In a linear equation, there are either one variable or more than one variable. Here is an example: x = 20 +15, find the value of “x”. 

Looking at the equation, it can be said that the value generated of the “x” needs to be equal to the number 35 as 20+15 = 35. The process through which the equation will be solved is termed “Solving equations.” 

Here is the standard form which is used for representing an equation – 

Ax + By = C. According to this equation, we need to find both x and y.

Solving Equations Involving Simplification 

An equation is solved to find the value of an unknown variable that the equation contains. In case the equation has the “equal to” sign, it is referred to as a balanced equation. Hence, it can be said that both the quantities on either side are equal. Let’s understand this with an example – 

We have an equation x – 4 = 5 

It can be said that x – 4 is the LHS equal to 5, the RHS. Here x is an unknown quantity. Therefore, we need to find the value of x. 

Here is the quick solution – 

x – 4 = 5 

x = 5 + 4 

x = 9 

How to Solve an Equation 

As mentioned earlier, an equation is a mathematical representation in which the two expressions in a variable need to have the same value. The solution of an equation can be described as the variable’s value to satisfy the equation. In order to solve all equations, we are supposed to perform the arithmetic operation for separating the variables. These include – 

• Adding the same number on both sides of an equation. 
• Subtracting the same number on both sides of an equation.
• Multiplying the same number on both sides of an equation.
• Dividing the same number on both sides of an equation.

Explain Linear Equation 

A linear equation can be described as an equation where there is the highest degree of power of one variable. In simple terms, no variable has an exponent of more than one in a linear equation. In a graph, a linear equation constantly forms a straight line. Hence, it is named the linear equation. 

• A linear equation in which only one variable is present, for example, Mx+N=0, where M and N are constant, and x is a variable.  
• A linear equation in which two variables are present, for example, Mx+Ny=O, where M, N, and O are constant and x and y are variables.

There are three ways in which the standard form of linear equations can be written. These include one variable, two variables, and three variables, and it is also called a general form of linear equation.

1. In one variable: px+q=0, where p and q ≠ 0 and integer. x is a variable.
2. In two variables: px+qy=r, where p, q, and r ≠ 0 are integers. x and y are variables.
3. In three variables: px+qy+rz=s, where p, q, r, and s ≠ 0 are integers. x, y, and z are variables.

Golden rules of solving equations 

1. The outcome of a linear equation cannot be changed if the same number is subtracted, added, divided, or multiplied into both sides of the equation.
2. The value of the variable generating an equation valid is named the solution or root of the linear equation. 
3. The graph of a linear equation in one or two variables constantly forms a straight line.

Conclusion 

In this article describing solving equations involving simplifications, we studied the concept of solving equations involving simplifications and linear equations in detail. We covered several other topics, such as steps to solve equations involving simplifications and golden rules of solving equations. We hope this study material helped you better understand solving equations involving simplifications.