Neft Teacher · Learn It

Unit 6 · Standard 6.AT.7

Simplify Algebraic Expressions

Lesson 6-15 · Learn It — how the math works

Why we're learning this

The music studio is placing supply orders for three rehearsal rooms. Room A needs 4 microphones and 3 stands. Room B needs 2 microphones and 5 stands. Room C needs 6 microphones and 1 stand. Instead of ordering separately, you can combine: (4 + 2 + 6) microphones and (3 + 5 + 1) stands = 12 microphones and 9 stands. That's simplifying by combining like items!

✱ Math Workbench

Learn It

How do we simplify by combining like terms?

Like terms are terms with the same variable raised to the same exponent, like 2x and 5x. To simplify an expression, you add or subtract the like terms to make it shorter.

Picture itSee what the math looks like before you read about it

A studio order lists the same equipment two different ways. On the left it is written out item by item — microphone, microphone, stand, microphone, stand. On the right the same gear is grouped together — 3 microphones and 2 stands.
Where you see this in real lifeA studio order lists the same equipment two different ways. On the left it is written out item by item — microphone, microphone, stand, microphone, stand. On the right the same gear is grouped together — 3 microphones and 2 stands.

Watch me solve itI do — read one step at a time

The problem looks like this
Tape diagram: 4m + 2m + 6m make 12m, and 3s + 5s + 1s make 9s.12microphones4269stands351
  1. The rooms need microphones and stands: (4 + 2 + 6) microphones and (3 + 5 + 1) stands.(4 + 2 + 6)
  2. Microphones are like items, so I add: 4 + 2 + 6 = 12 microphones.4 + 2 + 6 = 12
  3. Stands are like items, so I add: 3 + 5 + 1 = 9 stands.3 + 5 + 1 = 9
  4. In algebra this is the same as 4m + 2m + 6m + 3s + 5s + 1s = 12m + 9s.

Watch out — mistakes students make here

  • Adding 6x + 2x adds the coefficients — the exponent doesn't change. It stays 8x, not 8x².
  • 16x folds ALL the numbers into the x-term. Only 6x and 2x are like terms; 3 + 5 = 8 stays a constant.
  • The digits were pushed together. Combine like terms by adding: 6x + 2x = 8x and 3 + 5 = 8.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Let's 5x + 3x. Are these ?
  2. Yes, both have x, so we add the numbers in front:5 + 3 = 8
  3. So 5x + 3x = 8x.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Sort the into and not-like terms in the activity.
  • Remember: only with the same variable can be combined.

Solve: 7x + 3x.

My answer

Stuck? Open one hint at a time.

Hint 1

7x and 3x have the same variable x, so they're like terms and can combine.

Hint 2

Add the coefficients; the x stays exactly the same — no squaring, no multiplying coefficients.

Hint 3

Compute 7 + 3 and place that sum in front of x.

Check my answer
✅ Answer: 10x
7x + 3x = 10x. Add the coefficients: 7 + 3 = 10.

Turn & TalkSay it out loud with a partner

Three rooms need microphones and stands. Why can you add all the microphones together (4 + 2 + 6) but not mix microphones with stands?

Try starting with:

  • I can add the microphones because they are the ___ type.Puedo sumar los micrófonos porque son del ___ tipo.
  • I cannot mix microphones and stands because they ___.No puedo mezclar micrófonos y soportes porque ___.
Use these wordsLike TermsCombineSimplifyCoefficient