For more complex algebra equations, it might become necessary to combine like terms. These are terms that have the same variable and are raised to the same power. So, for example, So 2x, 12x, and ⅕x are like terms, but 2, 3x, x2, and ½y are not like terms. While this is a simple concept, it quite frequently tricks people taking the SAT math section.
Combining like terms in an equation is actually really simple. To start, choose one side to clean up, then do the other side. After that, it is just a matter of doing the opposite to both sides to get all the variables on one side of the equation and all of the numbers on the other side of the equation.
TIP: Numbers that come with a variable (like 12x or 13y) can NOT be combined with a regular number. So, for example, 2x and 12x and be combined, but 2 and 12x cannot be combined because they are unlike terms. Usually, questions that appear difficult are actually just testing the test taker's ability to recognize and combine like terms. By getting variables on one side of the equation and the numbers on the other, most problems become a lot simpler than they at first seem.
Solve for the Variable
To solve for a variable, simply follow the same directions above. However, in this case a single number will not be given at the end. That is, there may be a variable in the answer, which is fine when not using factoring.
For example:
Solve for x in terms of y. 3y + x = 42
To solve this equation correctly, it is important to get the variable asked for on one side of the equation.
3y + x = 42
-3y -3y
y = 42 - 3y
In the example above, there is no further simplified answer (without using factoring.) Because they are not like terms (42 and 3y), they cannot be combined.
TIP: It is important to read the question carefully and ensure that the right variable is being looked at. While it may seem obvious what a question is asking for at times, it is important to remember that test makers are out to trick test takers, so read the questions carefully and solve for the right variable.
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