In Part 3 of our lesson series on Algebra, this lesson focuses on solving for variables in equations. The key to solving for variables in algebraic equations is to understand how to isolate the variable by unwrapping all of the other operations. We need to get the variable we are solving for on one side of the equation, so that we can solve the basic math on the other side of the equation.
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Algebraic Equation Solve for Variable
The key to solving for variables in algebraic equations is to understand how to isolate the variable by unwrapping all of the other operations. We need to get the variable we are solving for on one side of the equation, so that we can solve the basic math on the other side of the equation.
Isolate variables by applying the opposite of each operator (for example, the opposite of multiplication is division and the opposite of addition is subtraction) both sides of the equation. This is called “cancelling” the operation because applying the equal and opposite operation cancels the original operation.
To eliminate an operation, apply the opposite operation
Always apply the same operation on one side of the equation on the other side of the equation
Confused? Don’t worry it will become much easier when you see an example
Example 1. Solve for x in the equation: x – 2 = 5
Step 1. Isolate the x. In order to isolate the x here, we need to remove the -2 from the left side of the equation. Do this by applying the opposite operation. The opposite of -2 is +2, so we need to add 2 to both sides of the equation.
x – 2 = 5
x – 2 + 2 = 5 + 2
x = 7
Let’s check out work by plugging our x back into our original equations
x – 2 = 5
7 – 2 = 5
5 = 5
Great! We know we got the correct answer
It is very important to remember that whatever you do to one side of an equation needs to also be done to the other side of the equation. For example, in the last problem if you had only added 2 to one side of the equation you would have come up with the wrong answer.
Example 2. Solve for x in the equation 2x – 1 = 3
Step 1: Isolate the x, start with addition/subtraction. To remove the -1 we have to add 1 to both sides
2x – 1 + 1 = 3 + 1
2x = 4
Step 2: Isolate the x, remove the multiplier or dividers next.
Step 3. Let’s check our work
2x – 1 = 3
2 * 2 – 1 = 3
4 – 1 = 3
3 = 3 check!
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