Algebra Solved Examples
Here we have provided some solved examples on algebra for your better understanding.
Example 1: Solve 3ex + 6 = 120
Solution:
Given,
3ex + 6 = 120
3ex = 120 – 6
3ex = 114
ex = 114/3
ex = 38
x = ln 38
Example 2: Solve for the value of y: 2(4-y)-3(y+3)=11
Solution:
2(4-y) -3(y+3)=11
8-2y-3y-9=11
-5y-1=-11
-5y-1+1=-11+1
-5y=-10
Dividing both the sides by -5,
-5y/-5=-10/-5
y=2
Example 3: Evaluate (2.3a5b2) × (1.2a2b2) when a = 1 and b = 0.5
Solution:
Let us simplify the given expression
=2.3a5b2 × 1.2a2b2
=2.3 × 1.2 × a5 × a2 × b2 × b2
=2.76 × a5+2 × b2+2
=2.76a7b4
Now let us substitute when, a = 1 and b = 0.5
For 2.76 a7 b4
= 2.76 (1)7 (0.5)4
= 2.76 × 1 × 0.0025
= 0.1725
Example 4: (2x-1)/3 – (6x-2)/5 = 1/3
Solution:
We have,
(2x-1)/3 – (6x-2)/5 = 1/3
By taking LCM for 3 and 5, which is 15
((2x-1)×5)/15 – ((6x-2)×3)/15 = 1/3
(10x – 5)/15 – (18x – 6)/15 = 1/3
(10x – 5 – 18x + 6)/15 = 1/3
(-8x + 1)/15 = 1/3
By using cross-multiplication, we get,
(-8x + 1)3 = 15
-24x + 3 = 15
-24x = 15 – 3
-24x = 12
x = -12/24 = -1/2
Verification
LHS = (2x – 1)/3 – (6x – 2)/5
= [2(-1/2) – 1]/3 – [6(-1/2) – 2]/5
= (- 1 – 1)/3 – (-3 – 2)/5
= – 2/3 – (-5/5)
= -2/3 + 1
= (-2 + 3)/3 = 1/3
RHS
Example 5: Find a number such that when 5 is subtracted from 5 times that number, the result is 4, more than twice the number.
Solution:
Let us consider the number as ‘x’
Then, five times the number will be 5x
And, two times, the number will be 2x
So,
5x – 5 = 2x + 4
5x – 2x = 5 + 4
3x = 9
x = 9/3 = 3
Also Read:
Algebra in Math: Definition, Branches, Basics and Examples
Algebra is the branch of mathematics that deals with symbols and the rules for manipulating these symbols. It is a unifying thread of almost all of mathematics and includes everything from solving elementary equations to studying abstractions such as groups, rings, and fields.
It helps represent problems or situations in the form of mathematical expressions. It is different from Arithmetic as Arithmetic deals with specific numbers and simple operations such as addition and subtraction. Algebra, on the other hand, introduces more complex operations and includes the use of variables, equations, and functions.
Table of Content
- What is Algebra
- Algebra Branches
- Algebraic Expressions with Examples
- Algebraic Equations
- Linear Equation
- Polynomial
- Sequence and Series
- Set Theory
- Vectors
- Relations and Functions
- Matrices and Determinants
- Exponential & Logarithmic functions
- Algebra Formula
- Algebraic Operations
- Algebraic Laws
- Algebraic Identities