Understanding Algebra

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Algebra is one of the most important topics in Mathematics and it covers a huge range of important sub-topics which are very much necessary to understand the higher concepts of the subject. Algebra covering basics of math is known as Elementary algebra and understanding this portion is very important in order to do well in the other parts of math. Understanding algebra is the first step in understanding math as algebra starts from basic topics such as finding LCM and GCF of numbers, solving equations, absolute value of numbers etc.

Example 1: Solve the given absolute value equation, |x – 4| = 10.

Given absolute value equation: |x – 4| = 10.

Since absolute value means distance of a number from ‘0’, it is always positive. Hence the above equation

splits into two ways:

They are (x– 4)= 10 and - (x– 4)= 10-> (x– 4)= -10.

Solve (x- 4)= 10 -> x= 10+ 4 -> x= 14

Solve (x– 4)= -10 -> x= -10+ 4 -> x= -6.

Hence we get: x = 14 and x = -6.

Example 2: Find the midpoint between the two points (3, 4) and (5, 6).

Given two points: (3, 4) and (5, 6).

To calculate the midpoint betweenthe two points (x1, y1) and (x2, y2), we use the midpoint formula, given as:

Midpoint = [(x1 + x2)/ 2, (y1 + y2)/2]

Applying the above midpoint formula for the given two points, we get:

Midpoint = [(3 + 5)/2, (4 + 6)/2] = (8/2, 10/2) = (4, 5).

Therefore midpoint between the two points is (4, 5).