Basic Algebra Calculations

Introduction to basic algebra calculations:

Basic algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. The part of basic algebra calculations called elementary algebra calculations is often part of the curriculum in secondary education and introduces the concept of variables representing numbers. The variables are manipulated using the rules of operations that apply to numbers, such as addition. (Source: Wikipedia).

Examples for basic algebra calculations:

Example 1 for basic algebra calculations:

Find the value for x in (x+2) +(x-22) +(x+45) =0.

Solution:

The given expression is(x+2) +(x-22) +(x+45) =0.

In this above expression first add the constants separately and then add the variable x.

(x+2) +(x-22) +(x+45) = (x+ x+ x) + (2-22+45)

(x+ x+ x) + (2-22+45) =3x+25

3x+ 25=0

3x =-25

x=-25/3

The value for x in (x+2) +(x-22) +(x+45) =0 is -25/3.

Example 2 for basic algebra calculations:

Find the value for the quadratic equation x ^2+6x +8=0.

Solution:

The given quadratic equation is x ^2+6x +8=0.

We have to find the roots for the above quadratic equation.

This can be solved by the factoring by middle term.

A=co-efficient 0f x ^2=1

B= co- efficient of x=6

C= constant=8

We split the 6 as (2+4), and then only we get 2 x4 =8.

x ^2+6x +8= x ^2+2x+4x +8

Take x as common in first two terms and 4 as common in next two terms.

x ^2+6x +8= x(x+2)+4(x+2)

x ^2+6x +8= (x+4) (x+2)

(x+4) (x+2) =0

x+4 =0 and x+2 =0

In the equation x+4 =0, subtract 4 on both sides.

x+4 =0

x+4-4 =0-4

x=-4

In the equation x+2 =0, subtract 2 on both sides.

x+2 =0

x+2-2 =0-2

x=-2

The roots for the equation x ^2+6x +8=0 is x=-2,-4.

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Practice problem for basic algebra calculations:

Find the value of x for the equation (x+12)+( x-22)=0
Answer: x=5.

Find the roots for the quadratic equation x ^2+ 11x+30=0.
Answer: x=-5,-6.