How to subtract variables

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ISEE Middle Level Quantitative Reasoning › How to subtract variables

Questions 1 - 10
1

Simplify:

Explanation

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:

2

Simplify:

Explanation

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.

3

Simplify the following expression

Explanation

Simplify the following expression

We can begin by grouping like terms:

Next, combine the like terms. In this case, simply treat them like two subtraction problems.

So our answer is:

4

Simplify:

Explanation

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:

5

Simplify:

Explanation

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.

6

Simplify:

Explanation

Begin by distributing the :

Multiply all factors:

Group together the only like factor ():

Combine like terms:

7

Simplify:

Explanation

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

8

Simplify:

Explanation

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:

9

Simplify:

Explanation

10

Simplify:

Explanation

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