Table of Contents

## CBSE Maths Notes

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### Chapter 4 – Simple Equations

A condition on a variable is referred to as an equation. Something that can change is referred to as a variable. It takes on several numerical values and does not have a fixed value. Letters from the English alphabet, such as x, y, z, l, m, n, p, and so on, are commonly used to represent these. We create expressions from variables by executing operations on them such as addition, subtraction, multiplication, and division.

**What Equation Is?**

A condition on a variable is referred to as an equation. The requirement is that both expressions have the same value. The variable must appear in at least one of the two expressions.

When the expressions on the left and right are swapped, the equation remains the same. This characteristic comes in handy when solving equations.

How to Solve an Equation

If we choose one of the following options for any balanced numerical equation:

- add the same number to both sides,
- or subtract the same number from both sides,
- or multiply by the same number to both sides,
- or divide by the same number on both its sides, the balance is undisturbed.

**More Equations**

Moving to the opposite side is referred to as transposing. It has the same effect as adding the same number to both sides of the equation (or removing the same amount from both sides).

We change the sign of a number when we move it from one side of an equation to the other.

**Applications of Simple Equations to Practical Situations**

We know how to convert statements in everyday language into simple equations. To solve the problems (or puzzles), we have to solve these equations by the usual method.

Equations involving only a linear polynomial are called simple equations.

e.g. 4x + 5 = 65,10y – 20 = 50

In an equation, there is always an equality sign.

A Simple Equation remains the same when the expression in the left and right are interchanged.

The value of a variable, which makes the equation a true statement is called the solution of a linear equation.

e.g. 5x – 12 = -2 is a equation

L.H.S = 5x – 12 = 5 × 2 – 12 = 10 – 12 = -2

L.H.S = R.H.S

In the case of the balanced equation, we have

- add the same number to both the sides,
- subtract the same number from both the sides
- multiply both sides by the same number
- divide both sides by the same number, the balance remains undisturbed,

ie. The value of the LHS remains equal to the value of the RHS.

Transposing means moving to the other side. Transposition of a number has the same effect as adding the same number to (or subtracting the same number from) both sides of the equation. When you transpose a number from one side of the equation to the other side, you change its sign. For example, transposing +3 from the LHS to the RHS in equation x + 3 = 8 gives x = 8 – 3 = 5.