Solve Linear Equations

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Linear equations are the equation where the highest degree of the variable is one. Simple linear equations are very commonly used in algebra and many other topics. There are various mathematical operations which are used to simplify the linear equations. In a linear equation there can be more than one variable but the condition is all the variable cannot have degree or power of the exponent more than one.

Example 1: Solve for the variable x in the equation 2(x – 2) =15?

Solution: Given equation is 2 (x – 2) = 15.
Here the unknown variable which needs to be solved for is x.
First step: Distribute 2 on one side of the equation.
This gives, (2x – 4) = 15.
Add 4 on both sides of the equation: 2x = 19.
Now dividing both sided of the equation by 2.
This gives 2x/2 = 19/2.
This reduces the given equation to x = 19/2.
Hence the solution is x = 9.5.
 
Example 2: Solve for the variable x in the equation 3(x – 1) -1 = 26?

Solution: Given equation is 3(x – 1) -1 = 26.
Here the unknown variable which needs to be solved for is x.
First step: Add 1 on both sides and distribute 3 to (x - 1) in the equation.
This gives, (3x – 3) = 27.
Add 3 on both sides of the equation: 3x = 30.
Now dividing both sided of the equation by 3.
This gives 3x/3 = 30/3.
This reduces the given equation to x = 30/3.
 
Hence the solution is x = 10.

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