Chapter 4: Simple equations

Chapter 4

Simple Equations

Introduction to simple equations

An equation is a statement of uniformity between two mathematical expressions containing one or more variables.
 Rules for simple equation,

e.g. 2x – 3 = 5, 3x + 9 = 11, 4y + 2 = 12

Two expressions on both sides of the equation should have equal value and at least one of the expressions must have a variable. An equation remains the same if the LHS and the RHS of the equation are interchanged.

Equation

An equation is a statement which states that two expressions are equal.

Solving an equation

The value of the variable for which the left hand side of an equation is equal to its right hand side is called the solution of that equation.
For example : For the equation, x + 2 = 6, x= 4 is the solution.

An equation remains unchanged if :

1. The same number is added to each side of the equation.
2. The same number is subtracted from each side of the equation.
3. The same number is multiplied to each side of the equation
4. Each side of equation is divided by the same non-zero number.

Solving an equation by shortcut method (transposing terms)In an equation if a positive sign is transported from one side to other, its sign becomes negative.

• In an equation if a negative sign is transported from one side to other, its sign becomes positive.
• In an equation if a term in multiplication is transported from one side to other, it goes in division.
• In an equation if a term in division is transported from one side to other, it goes in multiplication .
• While solving an equation with the variable on both the sides, transpose the terms containing the variable to one side and the constants on the other side.

Verbal statement vs algebraic statements

Example:

Kathir is twice taller than Krishna. That is Kathir height is two times larger than Krishna's height. Now, this is known as a verbal statement.
If you write the above verbal statement in an algebraic statement we get,
 Let the height of the Krishna is x.
 Therefore Kathir height = 2×HeightofKrishna=2×x=2x.
 In the above example, we understood that normally we use the verbal statement to mention any mathematical operation, then we translate this verbal statement to an algebraic statement to find the unknown value.
Now let's see a few examples of how we are using the verbal and algebraic statement in the mathematical operation.
[Note: In a verbal statement the unknown value x is represented as some number or a number].

Addition keywords: Sum, total, added, increased, more than, etc.

Subtraction  keywords: Minus, Decreased by, less than, the difference of, subtracted, etc.

Multiplication keywords: Multiplied by, The product of, Times, Thrice, Twice etc.

Division keywords: Divided by, The ratio of, The quotient of, etc.

Using these above, we can also make another operation that is,

 Equals keywords: Equals, Is the same as, yields.