# Algebra Linear Equations

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Algebra linear equations are always of form ax + b = 0 where x is considered as the variable in the equation and a and b are  real numbers. This form “ax + b =0” is called as the standard form of any of the linear equations. The variable can be any other alphabet too.

Let us take some examples of Algebra Linear Equations to understand the concept I a better way.

Example 1: - Solve the following equation
2 (3 + x) + 5 = 10x – 2 (x – 1)

Solution: - From the equation:-

2 (3 + x) + 5 = 10x – 2 (x – 1)

ð  6 + 2x + 5 = 10x – 2x + 2

ð  11 + 2x = 8x + 2

Subtracting 2 from both sides, we get

ð  11 + 2x – 2 = 8x + 2 – 2

ð  9 + 2x = 8x

Subtracting 2x from both sides, we get

ð  9 + 2x – 2x = 8x – 2x

ð  9 = 6x

Dividing both sides by 6, we get

9/6 = 6x/6

x = 3/2

Hence x = 3/2 is the solution of equation 2 (3 + x) + 5 = 10x – 2 (x – 1)

Example 2:  Solve the following equation for ‘m’
5 (m + 2) -10 = 8m – (3m + 7)

Solution:-  From the equation:

5 (m + 2) -10 = 8m – (6m + 9)

ð  5m + 10 – 10 = 8m – 6m – 9

ð  5m = 2m – 9

Subtracting 2m from both sides, we get

5m – 2m = 2m – 9 – 2m

3m = -9

Dividing both sides by 3, we get

3m/3 = -9/3

m = -3

Hence m  -3 is the solution of 5 (m + 2) -10 = 8m – (3m + 7).