grade 7 Linear Expression Calculation

Linear Expression Calculation

Working with linear expressions is tidying by grouping terms of the same kind. Just as 3 apples plus 2 apples make 5 while apples and oranges cannot be added, 3x and 5x combine but 3x and the constant 2 stay apart. With brackets, the distributive law spreads the multiplier over each term, then the coefficients of like terms add into ax + b. Change the extra x coefficient, the extra constant, and the multiplier k, and the square and circle pieces gather while the area picture shows why distribution works.

Combining Like Terms

Extra x coefficient2

Extra constant1

👀 What Are Like Terms?

①A linear expression has degree 1 in the letter (ax+b)

②Same letter and same degree: 3x and 5x are like terms

③Constants among themselves are like terms: 2 and -7

④3x and 3x² are NOT like terms (different degree)

Distributive Law

Multiplier k3

🔍 How Distribution Works

①k(a + b) = ka + kb

②Multiply each term inside the parentheses by k

③Think of it as a rectangle's area: whole = sum of parts

④Watch the sign carefully when k is negative!

Adding and Subtracting Linear Expressions

Addition of Linear Expressions

(ax + b) + (cx + d) = (a+c)x + (b+d)

Add coefficients of like terms

Subtraction of Linear Expressions

(ax + b) - (cx + d) = (a-c)x + (b-d)

Subtraction is adding the negative

💡 Computation Order

①Remove parentheses (mind signs)

②Group like terms

③Combine coefficients

④Write the final answer as ax + b

Work It Out

Example 1

Simplify 3x + 5 − x + 2.

Group like terms.

(3x − x) + (5 + 2)

Compute.

= 2x + 7

▸ 2x + 7

Add the coefficients of like terms (same letter).

Example 2

Simplify 2(3x − 1) − (x − 4).

Expand the brackets with the distributive law.

6x − 2 − x + 4

Collect like terms.

= 5x + 2

▸ 5x + 2

A minus before a bracket flips every sign inside.

Exam Key Points

Core of Linear-Expression Calculation

Combine like terms; use distribution to remove parentheses

Always identify like terms first, then simplify

Grade-7 school exam type

After simplifying 3(2x − 1) + 2(x + 4), what is the sum of the coefficient of x and the constant term?

①11

②12

③13

④14

⑤15

▸ ③ 13

Expand with the distributive law.

6x − 3 + 2x + 8

It simplifies to 8x + 5, so add coefficient 8 and constant 5.

8x + 5 ⇒ 8 + 5 = 13

🎯 Exam Key Points

①Like terms: same letter AND same degree

②A "-" in front of parentheses flips every sign inside

③Mind sign errors when multiplying by a negative

④Final form: ax + b (descending degree)

⑤0x = 0; if the x coefficient is 0, only the constant remains

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Algebraic Expressions

Linear Equations

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