By Andrew Kuhry-Haeuser, Carmenta Founder
1) The #1 rule to remember is that, no matter what, any operation you apply to one side of the equals sign must be applied to the other side of the equals sign, whether it’s addition, subtraction, multiplication, division, exponents, or roots.
2) What’s slightly harder is knowing when to apply a particular operation. The short rule is: Make your operation the opposite of what’s there. If a number is added within the equation, subtract it. If it’s multiplied, then divide it. The point of doing this is to…
3) “Cancel out” all individual operations within the equation, one by one, until the problem is solved, or in other words, you’ve managed to…
4) Isolate the variable. In a simple algebraic equation, this is the goal. (In some more complex equations, the goal will be to isolate two or more variables.) To “isolate a variable” means to move everything that isn’t the variable to the opposite side of the equals sign. To do this, work from the outside in, and at each stage perform addition or subtraction operations before multiplication or division operations, then exponent or root operations last.
The following are examples of solving for a variable by isolating it:
6) If you learn these rules and apply them to as many practice equations as possible, you’ll have mastered basic equations and will be ready to move on to more advanced ones. Fortunately, those equations follow the same rules. The only difference is that they have more steps.
If you would like more help in Algebra, I encourage you to consider hiring one of Carmenta Online PhD Tutors’ highly experienced Algebra tutors. We also have a large faculty of science, math, language, and SAT tutors. We go out of our way to provide each student with the individualized approach that he or she needs.
ABOUT THE AUTHOR
Magister Andrew Kuhry-Haeuser has a B.A. (Honors) in Latin from Gonzaga University. He is currently the Founder and Head of both Carmenta Online PhD Tutors and Grey Fox Tutors. Magister Andrew has taught a number of classes for Carmenta, including “Classical Literature” and all levels of Latin, Conversational Latin, and Ancient Greek. He has also tutored a wide range of subjects, including Latin, Ancient Greek, English, Writing, German, Algebra, Geometry, Trigonometry, Calculus, Geology, Physics, Biology, Chemistry, and History.
Click here to see Magister Andrew’s full profile on the Carmenta website.