﻿ Simple Equations - Definition, Concept, Method & Questions

# Simple Equations

## Table of Content

• How to Solve Simple Equations?
• A simple equation is a mathematical statement consisting of an equal sign (=) and expressions on either side of it, used to determine the value of an unknown quantity.
It involves an unknown value or variable that needs to be determined. The goal is to find the value of the unknown variable that satisfies the equation and makes it true.
In a simple equation, the unknown value is typically represented by a variable, often denoted as "x" or "y." The equation may include numbers, constants, and arithmetic operations such as addition, subtraction, multiplication, and division.

### Variable

Variable is an unknown number that could have a different numerical value. A variable has no fixed value.

Example: It is represented by alphabetical letters like x, y, a, b etc.

### Constant

A constant is a value or number that never changes in expression; it’s constantly the same.

Example: 22, 3, 5 etc.

## How to Solve Simple Equations?

Here is an example of how to solve a simple equation:

Example: Solve the equation 3x + 2 = 8.

Solution:

Step 1: Subtract 2 from both sides of the equation
3x + 2 - 2 = 8 - 2
3x = 8 - 2
3x = 6

Step 2: Divide both sides by 3.
3x/3 = 6/3
x = 6/3
x = 2

Step 3: Verify the result by substituting back to the original equation.
3x + 2 = 8
3(2) + 2 = 8
6 + 2 = 8
8 = 8

The equation is true, so x = 2 is the solution.

NOTE: Keep in mind that solving equations using the above steps only works when the equation is a simple equation, if the equation is a complex equation, other methods such as transposition, systematic method and trial-and-error method may be used.

## Some Useful Methods to Solve Simple Equations

1. Trial-and-Error Method:

• This method means you try different numbers for "x" until you find one that works.
• It's not the quickest way, but it can help with simple equations.

Example: Solve for "x" in the equation: 2x + 3 = 9.

You can start by testing different numbers for "x":

• If you try x = 1, then 2(1) + 3 = 2 + 3 = 5 (not the same as 9).
• But if you try x = 3, then 2(3) + 3 = 6 + 3 = 9 (matches 9).

So, the solution is x = 3.

2. Systematic Method:

• In this method, you do things step by step to get "x" alone on one side of the equation.
• You do the same thing to both sides to keep the equation balanced.

Example: Solve for "x" in the equation: 4x - 7 = 17.

Start by getting "x" by itself step by step:

• Add 7 to both sides: 4x - 7 + 7 = 17 + 7
• That gives you 4x = 24
• Now, divide both sides by 4: 4x / 4 = 24 / 4
• That leaves you with x = 6

So, the answer is x = 6.

3. Transposition Method:

• This method is about changing the equation so that "x" is all by itself on one side.
• You do this by doing the opposite of what's in the equation.

Example: Solve for "x" in the equation: 3x/2 + 5 = 11.

Use transposition to get "x" alone:

• First, take away 5 from both sides: 3x/2 + 5 - 5 = 11 - 5
• That gives you 3x/2 = 6
• Now, to make "x" completely alone, you do the opposite of dividing by 2/3, which is multiplying by 2/3.
• So, you multiply both sides by 2/3: (2/3) * (3x/2) = 6 * (2/3)
• After simplifying, you get x = 4

So, the answer is x = 4.

## Quick Video Recap

In this section, you will find interesting and well-explained topic-wise video summary of the topic, perfect for quick revision before your Olympiad exams.

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