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:

Begin by multiplying through by :

Perform the multiplications:

The double negation becomes addition:

Group like terms:

Combine like terms:

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.

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