High School Math : How to combine like terms with negative numbers in pre-algebra

Study concepts, example questions & explanations for High School Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : How To Combine Like Terms With Negative Numbers In Pre Algebra

What is the value of \(\displaystyle -3 - (-5) + 9 + (-2)\)?

Possible Answers:

1

13

-1

8

9

Correct answer:

9

Explanation:

Adding and subtracting negative integers is confusing if you don't use parentheses right.  As long as you remember to keep them in the right places and stay neat, it is easy.  Subtracting negative numbers is the same as adding a positive number, and adding a negative number is the same as subtracting a positive number.  So, we could rewrite the equation like this:

\(\displaystyle -3+5 + 9 -2 = 9\)

Example Question #2 : How To Combine Like Terms With Negative Numbers In Pre Algebra

What is \(\displaystyle 3y+4x-18y+16x\) simplified?

Possible Answers:

\(\displaystyle 20x-15y\)

\(\displaystyle 13x+15y\)

\(\displaystyle 20x-21y\)

\(\displaystyle 20x+21y\)

Correct answer:

\(\displaystyle 20x-15y\)

Explanation:

To simplify a problem like the example above we must combine the like termed variables.

Like terms are the numbers that have the same variable, in this example,  and .

Separate the s to get \(\displaystyle 4x+16x\)

Then perform the necessary addition to get \(\displaystyle 20x\)

Then separate the ’s to get \(\displaystyle 3y-18y\)

Then perform the necessary subtraction to get\(\displaystyle -15y\)

We then combine our answers to have the simplified version of the equation \(\displaystyle 20x-15y\).

Example Question #3 : How To Combine Like Terms With Negative Numbers In Pre Algebra

If \(\displaystyle 3x+5=-2x\), what is \(\displaystyle x\)?

Possible Answers:

\(\displaystyle -1\)

\(\displaystyle -5\)

\(\displaystyle 5\)

\(\displaystyle 2\)

\(\displaystyle -3\)

Correct answer:

\(\displaystyle -1\)

Explanation:

Let's start with our equation, \(\displaystyle 3x+5=-2x\).

Subtract \(\displaystyle 3x\) from both sides:

\(\displaystyle 5=-2x-3x\)

Combine our \(\displaystyle x\)s:

\(\displaystyle 5=-5x\)

Divide both sides by \(\displaystyle 5\):

\(\displaystyle 1=-x\)

However, the problem is asking for \(\displaystyle x\) not \(\displaystyle -x\), so multiply both sides by \(\displaystyle -1\):

\(\displaystyle -1=x\)

Example Question #2 : How To Combine Like Terms With Negative Numbers In Pre Algebra

Simplify the following equation by combining like terms: \(\displaystyle 7X- 3Y+2X=18\)

Possible Answers:

\(\displaystyle XY=18\)

\(\displaystyle 9X-3Y=18\)

\(\displaystyle 7X+2X=3Y-18\)

\(\displaystyle 5X-3Y=18\)

\(\displaystyle 12X-Y=18\)

Correct answer:

\(\displaystyle 9X-3Y=18\)

Explanation:

X is the only term that appears twice in the equation.  Since both are positive numbers, we can add the X terms to simplify the equation. 

\(\displaystyle (7X-3Y+2X=18)=(9X-3Y=18)\)

Example Question #3 : How To Combine Like Terms With Negative Numbers In Pre Algebra

Combine the like terms for \(\displaystyle -5x+-3x-x\).

Possible Answers:

\(\displaystyle x\)

\(\displaystyle -x\)

\(\displaystyle -9x\)

\(\displaystyle -5x\)

\(\displaystyle -3x\)

Correct answer:

\(\displaystyle -9x\)

Explanation:

Remember, adding a negative number is the same as subtracting a positive number. That means we can think of this problem as \(\displaystyle -5x-3x-x\).

If we think of this on a number line, we start at \(\displaystyle -5x\), move left three units because of the \(\displaystyle -3x\), then move left again by one more unit for the \(\displaystyle -x\), giving us a total of \(\displaystyle -9x\).

Example Question #93 : High School Math

Simplify: \(\displaystyle -2x + 5 + (-4x) + (-6)\)

Possible Answers:

\(\displaystyle (-6x) + (-1)\)

\(\displaystyle 6x - 11\)

\(\displaystyle 6x -1\)

\(\displaystyle (-6x) - 11\)

\(\displaystyle -6x + 1\)

Correct answer:

\(\displaystyle (-6x) + (-1)\)

Explanation:

Here, we are interested in combining like terms. Like terms are those with the same variable,.

When combining terms with \(\displaystyle x\) in them, we add the coefficients. Thus, we have \(\displaystyle -2x + (-4x) = -6x\), and \(\displaystyle 5 + (-6) = -1\)

Therefore, we have \(\displaystyle -6x - 1 = -6x + (-1)\).

Example Question #3 : How To Combine Like Terms With Negative Numbers In Pre Algebra

Simplify:

\(\displaystyle 5-2x-4x+7-9x\)

 

 

Possible Answers:

\(\displaystyle 12+15x\)

\(\displaystyle 12+3x\)

\(\displaystyle 12-15x\)

\(\displaystyle 12-17x\)

\(\displaystyle 12-3x\)

Correct answer:

\(\displaystyle 12-15x\)

Explanation:

Combine like terms:

\(\displaystyle 5-2x-4x+7-9x\)

 = (5 + 7) + (-2x - 4x - 9x)

 = 12 + (-15x)

 = 12 - 15x

Example Question #4 : How To Combine Like Terms With Negative Numbers In Pre Algebra

Simplify:

\(\displaystyle 5x-2y+3x-6y\)

 

Possible Answers:

\(\displaystyle 2x-8y\)

\(\displaystyle 8x+8y\)

\(\displaystyle 8x-2y\)

\(\displaystyle 8x-8y\)

\(\displaystyle 2x-2y\)

 

Correct answer:

\(\displaystyle 8x-8y\)

Explanation:

To combine like terms, combine the numbers as you would a normal addition or subtraction problem:

\(\displaystyle -2y-6y\) \(\displaystyle = -8y\)

\(\displaystyle 5x +3x =8x\)

Therefore, \(\displaystyle 5x-2y+3x-6y\) = 8x - 8y.

Learning Tools by Varsity Tutors