In this chapter we will learn the concept of equation, its definition and some solved problems.
What is Equation in Math?
When a math expression contains equal to sign ” = ” , it is termed as an equation.
In equation, the expression present in left side of “=” symbol is equal to the right side.
Examples of equation;
(i) 4x + y = 6
The above expression contains ” = ” sign, hence its an example of equation.
Left side of equation is 4x + y
Right side of equation is 6.
The equation tells us that value of 4x + y is equal to 6.
(ii) 10x + 3y + x + 4 = 11
Since the expression contains ” = ” symbol, it is an example of equation.
Left side of equation is 10x + 3y + x + 4
Right side of equation is 11
The equation tells that value of 10x + 3y + x + 4 is equal to 11.
(iii) 6x + 2y + 3 = 11x + 1
The expression contains ” = ” sign, hence it is a math equation.
Left side of equation is 6x + 2y + 3
Right side of equation is 11x + 1
The equation tells that value of left side ( 6x + 2y + 3 ) is equal to the value of right side (11x+ 1)
(iv) 6x -7 + 4y
This expression is not an equation since it do not contain ” = ” sign.
Solving the equation
Solving the equation basically involves finding the values of variable to satisfy the given equation.
For Example
Consider the equation 2x + 3 = 9
To solve the equation you have to find the value of variable x so that left side becomes equal to right side.
Given below are steps to find x value.
Step 01
Take number 3 to right side. While taking number 3 to the right, the addition becomes subtraction.
2x + 3 = 9
2x = 9 – 3
2x = 6
Step 02
Take number 2 on right side. While taking number 2 on right, multiplication becomes division.
2x = 6
x = 6 / 2
x = 3
Hence for given equation, the value of x is 3.
Validation
Put x = 3 in the equation 2x + 3 = 9
2 (3) + 3 = 9
6 + 3 = 9
9 = 9
Hence both side equals 9. This means that for x = 3, the equation gets satisfied.
Equations – Solved Problems
(01) Solve the given equations
(i) y + 10 = 15
(ii) 9x + 4 = 31
(iii) z – 13 = 50
(iv) 4y – 7 = 13
(v) 3y -16 = 2
Solution
(i) y + 10 = 15
To solve the equation, we have to find the value of variable y.
Follow the below steps;
Step 01
Move number 10 to right side. On moving the number to other side, the addition becomes subtraction.
y + 10 = 15
y = 15 – 10
y = 5
Hence, the value of variable y is 5.
It means that when we put number y = 5, the equation will be satisfied.
(ii) 9x + 4 = 31
To find the value of x, follow the below steps;
Step 01
Move number 4 to right. While moving number to other side, the addition becomes subtraction.
9x + 4 = 31
9x = 31 – 4
9x = 27
Step 02
Move number 9 to right. Here the multiplication becomes division.
9x = 27
x = 27 / 9
x = 3
Hence, the value of x is 3.
(iii) z – 13 = 50
Here we have to find the value of variable z.
Move number 13 to right.
While moving other side, the subtraction becomes addition.
z – 13 = 50
z = 50 + 13
z = 63
Hence, the value of variable z is 63.
(iv) 4y – 7 = 13
Here we have to find the value of variable y.
Follow the below steps;
Step 01
Move number 7 to right.
While moving, the subtraction becomes addition.
4y = 13 + 7
4y = 20
Step 02
Move number 4 to right.
Here the multiplication becomes division.
4y = 20
y = 20/4
y = 5
Hence in given equation, the value of variable y is 5.
(v) 3y -16 = 2
To find value of y, follow the below steps.
Step 01
Move number 16 to right.
While moving the subtraction becomes addition.
3y – 16 = 2
3y = 2 + 16
3y = 18
Step 02
Now move number 3 to right.
Here the multiplication becomes division.
3y = 18
y = 18 / 3
y = 6
For given equation, the value of y is 6.