Simple equations

Simple Equations

1. Simple Equations
What is an Equation?
A condition of equality between two
mathematical expressions.

2. Framing an equation:
Example: Twice a number say x is added to
3 to get 7.
=> 2x + 3 = 7.
2 is the coefficient of x.
x is the variable.
3 and 7 are the constant terms.
(=) is the sign of equality.

3. Properties of an Equation.
The value of the variable for which the
equation is satisfied is called the solution of
the equation.
An equation remains the same if the L.H.S
and the R.H.S are interchanged.
In case of the balanced equation , if we add
subtract , multiply, divide both sides by the
same number, the balance remains
undisturbed i.e the value of L.H.S remains
equal to the value of R.H.S.

4. Solved example: addition.

5. Solved example:(subtraction
and division)

6. Solved example:
(subtraction & multiplication)

7. Transposition:
The process of moving a term from one side of the
equation to the other side is called transposing. It is the
same as adding and subtracting a number from both sides
of the equation.
Ex. Solve 5x + 9 = 19
=> Transposing 9 to the other side we get,
=> 5x = 19 – 9
=> 5x = 10
Transposing 5 to the other side we get,
x = 10/5
x = 2
.

9. Word problems of simple
equation:
Q1.The denominator of a fraction exceeds the numerator by 5. If 3
be added to both, the fraction becomes 3/4. Find the fraction.

Solution :
Let "x" be the numerator.
"The denominator of the fraction exceeds the numerator"
From the above information,
Fraction = x / (x + 5) ----------(1)

"If 3 be added to both, the fraction becomes 3 / 4"
From the above information, we have
(x+3) / (x + 5 + 3) = 3 / 4

10. Simplify.
(x + 3) / (x + 8) = 3/4
4(x + 3) = 3(x + 8)
4x + 12 = 3x + 24
x = 12
Plug x = 12 in (1)
Fraction = 12 / (12 + 5)
Fraction = 12 / 17
Hence, the required fraction is 12 / 17.

11. Q2.If thrice of A's age 6 years ago be subtracted from twice his
present age, the result would be equal to his present age. Find A's
present age.

Solution :
Let "x" be A's present age.
A's age 6 years ago = x - 6
Thrice of A's age 6 years ago = 3(x-6)

Twice his present age = 2x
Given : Thrice of A's age 6 years ago be subtracted from twice his
present age, the result would be equal to his present age.
So, we have
2x - 3(x - 6) = x

12. Simplify.
2x - 3x + 18 = x
- x + 18 = x
18 = 2x
Divide both sides by 2.
9 = x
Hence, A's present age is 9 years.

13. Q3.The fourth part of a number exceeds the sixth part by 4. Find
the number.
Solution :
Let "x" be the required number.
Fourth part of the number = x/4
Sixth part of the number = x/6
Given : The fourth part of a number exceeds the sixth part by 4.
x/4 - x/6 = 4
L.C.M of (4, 6) is 12.
(3x/12) - (2x/12) = 4
.

14. Simplify.
(3x - 2x) / 12 = 4
x / 12 = 4
Multiply both sides by 12.
x = 48
Hence, the required number is 48.