Algebra Solving Equations for an Unknown Quantity

Addition and subtraction are inverse operators of each other, as are multiplication and division. Usually, a problem will involve solving an equation for some variable. You want to convert the equation into the form x = some number (or some expression). Therefore, when you want to isolate a variable (i.e., solve the equation ), you need to undo any operations that are tying up the variable by applying the inverse operation. That is, if the variable is multiplied by a number, you need to divide both sides of the equation by that number. If a variable is divided by some number, you need to multiply both sides of the equation by that number. This eliminates that number from the variable by converting it into a 1. Since 1 is the multiplicative identity element, you can ignore l s that are involved in multiplication or division. If some number is added to the variable, you need to subtract that number from both sides of the equation. If some number is subtracted from the variable, you need to add that number to both sides of the equation. This eliminates that number from the variable by converting it into a zero. Since zero is the additive identity element, you can ignore zeros that are involved in addition or subtraction. 

The critical thing to remember, though, is that whatever you do to one side of the equation, you have to do the other side. Think of it as being fair. If you add a number to one side, you have to add the same number to the other side otherwise the equation would no longer be balanced. 

On your calculator, first enter the number on top (the numerator) and then divide by the number on the bottom (the denominator). Division operators are not commutative (i.e., a 4- b b 4- a), so the order in which you enter the numbers is critically important. On the other hand, multiplication and division are associative, so you can regroup fractions multiplied by a quantity. For example  

Division signs (4-) are rarely used in the sciences. Usually, a division operation is signaled by a fractional notation. Just think of the horizontal bar as the division sign. For example, if x divided by 15 equals 180, what does x equal  

Sometimes the variable is in the denominator. Since anything in the denominator denotes the division operation, you can undo the division by multiplying, which is the inverse operation. For example  

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