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# Equation - Equation Two expressions set equal to each other...

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Equation Two expressions set equal to each other Linear Equation An equation that can be written in the form ax + b = 0 where a and b are constants Note that the exponent ( definition found in Tutorial 2: Integer Exponents ) on the variable of a linear equation is always 1. The following is an example of a linear equation: Solution A value, such that, when you replace the variable with it, it makes the equation true. (the left side comes out equal to the right side) Solution Set Set of all solutions

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Solving a Linear Equation in General Get the variable you are solving for alone on one side and everything else on the other side using INVERSE operations. The following will give us the tools that we need to solve linear equations. Addition and Subtraction Properties of Equality If a = b, then a + c = b + c If a = b, then a - c = b - c In other words, if two expressions are equal to each other and you add or subtract the exact same thing to both sides, the two sides will remain equal. Note that addition and subtraction are inverse operations of each other. For example, if you have a number that is being added that you need to move to the other side of the equation, then you would subtract it from both sides of that equation. Example 1 : Solve for x . View a video of this example *Inverse of sub. 10 is add. 10
Note that if you put 8 back in for x in the original problem you will see that 8 is the solution to our problem. Example 2 : Solve for x . View a video of this example *Inverse of add. 7 is sub. 7 Note that if you put -12 back in for x in the original problem you will see that -12 is the solution we are looking for . Multiplication and Division Properties of Equality If a = b, then a(c) = b(c) If a = b, then a/c = b/c where c is not equal to 0.

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Equation - Equation Two expressions set equal to each other...

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