Page 12 - Algebra

Worked Example
Find the solution of 5x – 4 = 11
Solution:
Add 4 on both sides using the addition property
x =3
5x – 4 + 4 = 11 + 4
5x = 15
Worked Example
The sum of the two numbers is 84. If one of the numbers is 12 more than the other, find the two
numbers.
Solution:
Let the first number be x
The second number be x + 12
Sum of numbers = 84
x + x + 12 = 84
2x = 84 – 12
2x = 72
x = 36
Second number = x + 12 = 36 + 12 = 48
The numbers are 36 and 48.
2.3. Equation With No Solution
You might come across many equations that have no solution. It means that there is no value for the variable for which the equation holds true. We term such an equation as identity.
Worked Example
Find the solution to the given equation
6(x – 2) – x = 5(x – 4)
Solution:
Solve the equation like a normal equation
6(x – 2) – x = 5(x – 4)
6x – 12 – x = 5x – 20
5x – 12 = 5x – 20
12 = 20
The above statement doesn’t hold true.
So, the equation has no solution.
Page 11 of 177
Algebra I & II