Equivalent expressions: distributing and combining like terms

About this lesson

Grade 7 › Expressions, equations and inequalities

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Equivalent expressions: distributing and combining like terms

Warm-up

Three quick questions from earlier lessons.

Discover

Is $10 - (3 + 2)$ the same as $10 - 3 + 2$ ?

No
Yes

Key idea

Equivalent expressions are equal for every value of the variable.

Distribute:

a(b + c) = ab + ac

, also with minus signs:

-(b - c) = -b + c

. Combine like terms by adding their coefficients, keeping each term's sign:

5x - 2x = 3x

. Think of subtraction as adding the opposite.

Worked example

Simplify $6x - 2(x - 4) + 1$ .

6x - 2x + 8 + 1

−2 times each term.

4x + 9

Combine.

Your turn, guided

Your turn: the coefficient of $x$ in $7x + 3 - 2x$ .

5

7 − 2.

Practice ★

Write $7(x - 3)$ without parentheses. What is the constant term?
Write $3(x - 7)$ without parentheses. What is the constant term?

Combine like terms in $9x + 6 - 11x + 4$ . What is the coefficient of $x$ ?

Watch out!

Practice ★★

Simplify $6x - (5x - 2)$ . What is the constant term?
Simplify $7x - (9x - 9)$ . What is the constant term?

Boss problem. A rectangle has sides $x + 6$ and $3x - 5$ . Its perimeter is $2(x + 6) + 2(3x - 5)$ .

Exit ticket

Three questions to check you have got it.

Write $7(x - 3)$ without parentheses. What is the constant term?
Write $3(x - 7)$ without parentheses. What is the constant term?
Write $3(x - 2)$ without parentheses. What is the constant term?

Summary card

Equivalent expressions

Distribute to every term; combine like terms with their signs.

Watch out: a minus before parentheses changes every sign inside.

End of the lesson

Next lesson: Solve linear equations in one variable Back to the chapter

Answers: Equivalent expressions: distributing and combining like terms

A

$-21$
$-21$

B

$-2$

C

$2$
$9$

D

$3$

E

$-21$
$-21$
$-6$

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