Would I combine like terms?

Question

In the equation 3n +3 > 6n +8 - 3n, would I combine like terms, such as 6n and 3n on the left side of the equation? If so, what would I do afterwards?

Answer 1

Hey Danielle!

Good question. Usually for my Algebra students to solve for a variable I give them a 4 step process:

1. Multiply/Divide both sides by the same number
2. Add/Subtract the same number to both sides
3. Combine Like Terms
4. Distribution

Once you know these steps, in most cases, you try to apply them in reverse order -- in other words, start with 4 (if you can) and count down. In this case since there are no parentheses there is no distribution. Therefore we go to step 3, Combine Like Terms. This happens on the right side where there are two "n" terms.

Combining +6n and -3n gives us positive 3n.

The inequality now looks like this:

3n +3 > 3n +8

Assuming the problem wants you to determine whether the inequality is true (an equation has an equal sign instead of a greater than symbol) then we must further simplify. Now you go to step 2 and subtract 3n from both sides.

See if you can solve it from there!

Answer 2

Do as you do with equation - add/subtract from both sides, multiply/divide by left and right by the same number (with the only exception that when you multiply by negative number the inequality changes direction).

Your first step is good:

3n + 3 > 3n + 8

Now, subtract 3n from both sides. You will get

3 > 8

Well, in this particular case - it is impossible, doesn't matter what "n" is. So the answer - no solution!