Intro to Expressions and Equations

Combining Like Terms

Group and add terms with the same variable: 5x + 3 + 2x simplifies to 7x + 3.

Example

Group matching variable terms and add their coefficients. Only terms with the exact same variable part describe the same kind of quantity, so those are the ones we can combine. Adding their coefficients bundles repeated copies of that quantity into one term, which shortens the expression without changing the value it represents for any input.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

5x+3+2x5 x+ 3 + 2 x
Start with 5x + 3 + 2x.xxxxx+111+xx5x + 3 + 2xOnly tiles with the same variable part can combine.

Step 2 — Group like terms

Group the x terms: 5x and 2x.

(5x+2x)+3( \hl{5} x+ \hl{2} x)+ 3
Sort x-terms with x-terms, and constants with constants.x-termsconstantsxxxxxxx1115x and 2x are like termsThe constant tiles stay separate because they do not have x.

Step 3 — Add coefficients

Add coefficients: 5 + 2 = 7.

(5+2)x=7x( 5 + 2 )x= \hl{7} x
Add x coefficients only: 5 + 2 = 7.x-termsconstantsxxxxxxx1115 + 2 = 7, so the x-bin is 7xThe x-bin has 7 total x-tiles.

Step 4 — Result

Read the final result.

7x+37 x+ 3
The simplified expression is 7x + 3.x-termsconstantsxxxxxxx1115 + 2 = 7, so the x-bin is 7x7x + 37 x-tiles and 3 constant tiles remain.
combine-like-terms Like terms share the same variable part: - Identify terms with the same variable. - Add their coefficients. - Constants stay separate.