Algebra Introduction

In this page we are going to learn about algebra introduction concept. Study of relations and properties in the introduction of practice the algebra is the quantity of using the letters and other symbols is called algebra. This can be applicable to the relations which are true to the every kind of the magnitude. In the introduction of algebra, a set is defined as the pair of binary operations. Usually, set and operations includes the identity element. Operations given are commutative or associative property.

Algebra helps us to do the manipulation with variables. Variables are unknown values,we take it as x, y, z, w.......There are many branches under algebra like Elementary algebra, abstract algebra, Linear algebra, algebraic geometry, algebraic combinatories...etc...... In one sence all branches in mathematics is related to algebra. Complicated word problems can be easly solved with the help of algebra. Learn algebra in detail from tutorvista.

Equation is defined as the statement in which the two numbers or expressions should be equal. Equations are mainly used for the relation of variables and the numbers given in the statement. Many of the word problems are easily to be write down as the equations if there is little practice. Most of the simple rules are exist for simplifying the equations.

For Practice the following are the examples of equations are given in algebra:

1. 17 = 2 + 15
2. x = 7
3. 7 = x
4. t + 3 = 8
5. 3 × n +12 = 100
6. w + 4 = 12 - w
7. y - 1 - 2 - 9.3 = 34
8. 3 × (d + 4) - 11 = 321 - 2³

As given in the introduction of algebra, the following example is,

Example:

Translate the word problem into a proper equation

My age in years y plus 10 is equal to two times my age, minus 5.

The first expression with the stands for "my age in years plus 10", which is y + 10.

This is equal to the second expression for the "two times my age, minus 5.", which is 2 y - 5.

Setting these two expressions is equal to the one another gives us the equation:

y + 10 = 2 y - 5

Solving algebraic expression is nothing but finding the value of unknown variables in the expression like, x, y, w...

When solving the variable, we have to get a solution like x = 3 or z = 2001. When a variable is divided by some number, then we can use multiplication on both sides for solving that variable.

Practice Example:

Solve problem in algebra, x in the given equation x ÷ 6 = 5.

Since x on the left side is divided by 6, the equation is same as x * $\frac{1}{6}$ = 5. Then multiplying both sides by 6 we will cancel the $\frac{1}{6}$ on the left side:

x * $\frac{1}{6}$ * 6 = 5 * 6

x * 1 = 30

x = 30.