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In Algebra a variable is an unknown quantity written as a letter.

In order to solve for the unknown variable, you must isolate the variable. In order to isolate the variable you use the reverse of the order of operations ( PEMDAS.) Why reverse PEMDAS or SADMEP? In order to isolate the variable you have to undo the operations done to the variable.

When solving for a variable remember these three rules.

Isolate the variable

Whatever operation you perform on one side of the equation must be performed on the opposite of the equation.

Your order of operations becomes SADMEP

S=Subtract A=Addition D=Division M=Multiplication E= Exponent P=Parentheses

Let's apply these rules in an example involving a perimeter formula.

P = 2l + 2w and we want to solve for l

Step 1. Isolate the variable l by subtracting 2w from each side.

P -2w = 2l +2w

-2w

Step 2. P -2w = 2l

Now we continue to isolate for l by dividing by 2 (Remember the same task must be performed to both sides)

p - 2w/2 = 2l/2

P-w = l Solution

Notice in the example above we,

Isolated the variable

Performed the same operation to both sides

Used SADMEP

Pre-Algebra/Expressions,Equations,Integers

Pre-Algebra/Fractions,Percents

Algebra/Exponents,Equations,Radicals

Transcript

Today we are going to take an example of solving for a variable. We have half, base times height equals area. Hopefully you recognized this as the area of a triangle. We are going to solve for B or solve for the base. Now the steps to solve for a variable are as follows. First we are going to underline the variable that we are solving for. We are going to underline B and then use the reverse of please excuse my dear aunt sally. We are going to add and subtract first, multiple and divide next, and then any exponents then any parenthesis. So let’s work through our steps. OK let’s first underline the B ok that is what we are solving for. We next have multiplication and multiplication so we have to undo two multiplications and we will have to divide. Now if you are comfortable with multiplying with reciprocals that is the easiest way to get rid of a coefficient fraction. I’m going to multiply each side by two over one so I’m just going to multiple by the reciprocal of one half. So I end up with two over two so they just cancel out and if I multiply the left side by two then I have to multiply the right side by two over one which is just two So what I’m I left with after I multiply by the reciprocal? I’m left with base times height is equal to A times two. I like to put my coefficient first so I’m going to put a two times A. Now we have to get rid of the H because we are trying to get the B by itself. This is multiplication. How do we get rid of multiplication? We divide. Divide both sides by H and now we have the B by itself. So B is equal to two A over H and there is your answer.