Each step to the solution of an algebra problem usually involves an elementary arithmetic function such as addition, subtraction, multiplication, or division. For more complicated problems, getting to the solution may also involve trigonometric functions, powers, roots, and/or logarithms. Working a problem "step by step" means that you perform one of these operations at each step in order to get to the next step.
Working out an algebra problem consists of several steps in itself.
1) Clearly identify the information that is given. Know what it means, what the units are, and how the various pieces of information relate to each other.
2) Clearly identify the required solution, what units it needs to have, whether it is symbolic or numeric, whether it is one of many, and/or whether it must satisfy certain constraints or demonstrate a certain precision.
3) Formulate a method for getting from the given information to the required solution. If the first two steps are done properly, this may be fairly easy to do. Sometimes, it requires some research. (You may have to actually read and understand your textbook or other tutorial information.)
For some simple "solve for the variable" kinds of problems, the procedure usually required is to "undo" what has been done to the variable. If the variable has been multiplied by some number or expression, you likely must divide by that number or expression. If some number or expression has been added, you likely must subtract that. Whatever you do, be sure to do it to both sides of the equation.
Example
Given: 6x + 3y = 60
Find: Y in terms of x
Solution:
subtract 6x from both sides
6x + 3y - 6x = 60 - 6x
collect terms
3y = 60 - 6x (6x-6x=0; 3y+0 = 3y)
divide both sides by 3
3y/3 = 60/3 - (6/3)x
simplify
y = 20 - 2x (this is the desired solution)
Working out an algebra problem consists of several steps in itself.
1) Clearly identify the information that is given. Know what it means, what the units are, and how the various pieces of information relate to each other.
2) Clearly identify the required solution, what units it needs to have, whether it is symbolic or numeric, whether it is one of many, and/or whether it must satisfy certain constraints or demonstrate a certain precision.
3) Formulate a method for getting from the given information to the required solution. If the first two steps are done properly, this may be fairly easy to do. Sometimes, it requires some research. (You may have to actually read and understand your textbook or other tutorial information.)
For some simple "solve for the variable" kinds of problems, the procedure usually required is to "undo" what has been done to the variable. If the variable has been multiplied by some number or expression, you likely must divide by that number or expression. If some number or expression has been added, you likely must subtract that. Whatever you do, be sure to do it to both sides of the equation.
Example
Given: 6x + 3y = 60
Find: Y in terms of x
Solution:
subtract 6x from both sides
6x + 3y - 6x = 60 - 6x
collect terms
3y = 60 - 6x (6x-6x=0; 3y+0 = 3y)
divide both sides by 3
3y/3 = 60/3 - (6/3)x
simplify
y = 20 - 2x (this is the desired solution)
