# Linear Equation Solver

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In order to solve a Linear Equation in one variable of the type ax + b = 0 where a is not equal to 0 we distribute the terms within parenthesis and simplify both sides by collecting the like terms. Then we isolate all variables on one side and all the constants on the other side. We simplify and make the coefficient of the unknown variable 1.

Example 1: Solve:
5 – 3 (5x + 2) = 4 (7- 3x) + 1

Solution:
5 – 3 (5x + 2) = 4 (7- 3x) + 1
5 – 15x – 6 = 28 – 12x +1               [Distributing the terms within parenthesis]
-15x -1 = -12x + 29                         [On Simplifying the like terms we get]
- 15x + 12x = 29 + 1                       [Isolating the variable on one side and the constant on other side]
(- 3)x = 30                                         [Divide both sides by -3 and we will get]
x = -10

Example 2:
The sum of two numbers is 90 and the greater number exceeds thrice the smaller by 14.Find the numbers.

Solution:
Let the smaller number be x.
As the sum of the two numbers is 90, then the greater number will be 90 – x.
Thrice the smaller number will be 3x
So the equation becomes:
90 – x = 3x + 14
-x -3x = 14 – 90                             [Isolating the variable on one side and the constant on other side]
(-4)x = - 76                                       [Divide both sides by -4 and we will get]
x = 19
Then the greater number will be 90 – x = 90 – 19 = 71
Hence the two numbers are 19 and 71.