Add and Subtract Linear Expressions

Students add and subtract linear expressions with rational coefficients by combining like terms. They understand that like terms share the same variable and exponent, and apply rules for adding and subtracting signed rational numbers to coefficients.

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Grade 7 · Expressions and Equations · question 1 of 3

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(2x + 4) + (9x − 7) = 11x −

How it is taught

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Like terms share the same variable part.

Coefficients of like terms combine.

Numbers without a variable combine with each other.

Read it: Combining like terms

(2x + 5) + (4x − 8) in tiles: the x-tiles join, 2x + 4x = 6x. 5 positive units and 8 negative units make 5 pairs of 0, and 3 negative units are left, so the sum is 6x − 3.

Put the x-tiles together: x-tiles join only x-tiles.
Pair each positive unit with a negative unit: each pair makes 0.
The x-tiles and the units left over are the sum.

An x-tile and a unit are different sizes, so 2x and 5 never join: 2x + 5 stays two terms.

A positive unit and a negative unit are opposites, and opposites make 0. Here 5 pairs make 0 and 3 negative units are left.

So the sum has one x term and one number: 6x − 3.

Add x's to x's and numbers to numbers. An x and a number never join.

Joining an x and a number: 2x + 5 = 7x.

Only like tiles join: 2x + 4x = 6x, and the units leave 3 negative, so 6x − 3.

(2x + 2) + (3x − 4) = 5x − ___ — 2. x-tiles: 2x + 3x = 5x. Units: 2 positive and 4 negative, 2 pairs make 0, and 2 negative units are left: 5x − 2.

(3x + 4) + (2x − 7)

Today we'll add two linear expressions. The trick is to combine like terms — terms that share the same variable.

Here's our problem: three x plus four, all added to two x minus seven.

Both groups are being added, so we can drop the parentheses.

Look for like terms. Three x and two x both have the variable x — they're like terms. Four and negative seven are just numbers — like terms too.

Grade 7 · Combine like terms

We can shuffle the order to group like terms together: three x plus two x, then plus four minus seven.

Add the x-terms: three x plus two x is five x.

Add the constants: four minus seven is negative three.

Put them side by side. Our simplified expression is five x minus three.

Five x minus three! Same expression, much simpler. Like terms only mix with like terms.

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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