How to subtract variables - ISEE Middle Level Quantitative Reasoning

When solving this problem we need to remember our order of operations, or PEMDAS.

PEMDAS stands for parentheses, exponents, multiplication/division, and addition/subtraction. When you have a problem with several different operations, you need to solve the problem in this order and you work from left to right for multiplication/division and addition/subtraction.

Parentheses: We are not able to add a variable to a number, so we move to the next step.

Multiplication: We can distribute (or multiply) the .

Addition/Subtraction: Remember, we can't add a variable to a number, so the is left alone.

Subtract the numbers and keep the variable:

Answer:

This problem is as simple as it appears. All that you need to do is group together like terms:

The only like terms are the terms. Therefore, the simple answer is a matter of subtracting 3 from 4:

This problem is just a matter of grouping together like terms. Remember that terms like are treated as though they were their own, different variable:

The only part that might be a little hard is:

If you are confused, think of your number line. This is like "going back" (more negative) from 15. Therefore, you ranswer will be:

This problem really is a trick question. There are no common terms among any of the parts of the expression to be simplified. In each case, you have an independent variable or set of variables: and . Therefore, do not combine any of the elements!

Remember, when there is a subtraction outside of a group, you should add the opposite of each member. That is:

That is a bit confusing, so let's simplify. When you add a negative, you subtract:

Now, group your like variables:

Finally, perform the subtractions and get:

Begin by rewriting the subtracted group as a set of added negative numbers:

Now, simplify that a little by rewriting the additions of negatives as being mere subtractions:

Next, move the like terms next to each other:

Finally, combine like terms:

You need to begin by distributing the minus sign through the whole group . This gives you:

Simplifying the double negative, you get:

Now, you can move the like terms next to each other:

Finally, simplify:

First, start by distributing the subtraction through the terms in parentheses. Note that you will be subtracting negative numbers:

Subtracting a negative is the same as adding a positive:

Now, group the like terms:

All you need to do now is combine like terms:

Begin by distributing the subtraction through the parentheses:

Next, group the like terms:

Now, combine them:

Begin by putting similar variables together. Remember that combinations of variables such as are treated like a separate variable:

Combine like terms:

You can then rearrange the variables to get the answer as written:

Begin by distributing the subtraction through the group:

Next, change the double negative to a positive:

Begin by distributing the :

Multiply each factor:

Change the double negation to addition:

Combine like terms:

Begin by distributing the :

Multiply all factors:

Group together the only like factor ():

Combine like terms:

Begin by moving all like terms next to each other. Remember that you must treat every variable type separately:

Combine like terms:

You merely need to reorder the variables to get to the form in the answer choice.

Begin by distributing the through the group:

Next, perform the multiplications:

Group the like terms:

Combine like terms:

Rearrange the terms to get the answer as it appears in the answer choices.

Begin by multiplying through by :

Perform the multiplications:

The double negation becomes addition:

Group like terms:

Combine like terms:

When solving this problem we need to remember our order of operations, or PEMDAS.

PEMDAS stands for parentheses, exponents, multiplication/division, and addition/subtraction. When you have a problem with several different operations, you need to solve the problem in this order and you work from left to right for multiplication/division and addition/subtraction.

Parentheses: We are not able to add a variable to a number, so we move on to the next step

Multiplication: We can distribute the negative sign to the and

Remember, a negative times a negative will equal a positive, so we have a

Finally we can combine like terms