Subtracting Linear
Expressions
Name: ______________________
Date: _______________________
To _____________ one linear expression from another, ___________ the ____________ of ____________
______________ in the expression. You can use a ___________ or a ________________ method.
Find the difference.
a. (5x + 6) – (–x + 6)
Vertical Method: ____________ like terms _________________ and __________________.
(5x + 6)
– (–x + 6)
5x + 6
+ x–6
6x
Add the
opposite
Horizontal Method: Use properties of _____________ to _______________ _________________
_________________ and _____________________.
(5x + 6) – (–x + 6) = 5x + 6 + x – 6
Distributive Property
= 5x + x + 6 – 6
Commutative Property of Addition
= 6x
Combine like terms
We Do it Together!
Find the difference.
(7y + 5) – 2(4y – 3)
Vertical Method:
Horizontal Method:
Add the
opposite
You Do it!
Find the difference using either the vertical or horizontal method.
a. (m – 3) – (–m + 12)
b. –2(c + 2.5) – 5(1.2c + 4)
Subtracting Linear
Expressions
Name: ______________________
Date: _______________________
Real-Life Application
The original price of a cowboy hat is d dollars. You use a coupon and buy the hat for (d – 2) dollars.
You decorate the hat and sell it for (2d – 4) dollars. Write an expression that represents your
earnings from buying and selling the hat. Interpret the expression.
earnings = selling price – purchase price
= (2d – 4) – (d – 2)
= (2d + (–4)) + (–d + 2)
= 2d + (–d) + (–4) + 2
= d + (–2) = d – 2
Use a model.
Write the difference.
Add the opposite.
Group like terms.
Combine like terms.
You earn (d – 2) dollars. You also paid (d – 2) dollars, so you doubled your money by selling the hat for
twice as much as you paid for it.
On your Own
What if in the example above, you sell the hat for (d + 2) dollars. How much do you earn from
buying and selling the hat?
Subtracting Linear
Expressions
Name: ______________________
Date: _______________________
To subtract one linear expression from another, add the opposite of each term in the expression. You
can use a vertical or a horizontal method.
Find the difference.
a. (5x + 6) – (–x + 6)
Vertical Method: Align like terms vertically and subtract.
(5x + 6)
– (–x + 6)
5x + 6
+ x–6
6x
Add the
opposite
Horizontal Method: Use properties of operations to group like terms and simplify.
(5x + 6) – (–x + 6) = 5x + 6 + x – 6
Distributive Property
= 5x + x + 6 – 6
Commutative Property of Addition
= 6x
Combine like terms
We Do it Together!
Find the difference.
(7y + 5) – 2(4y – 3)
Vertical Method:
(7y + 5) Add the
–2(4y – 3) opposite
7y + 5
+ –8y +6
–y + 11
Horizontal Method:
(7y + 5) – 2(4y – 3) = 7y + 5 + (–2)(4y) + (–2)( –3)
= 7y + 5 + (–8y) + 6
= 7y + (–8y) + 5 + 6
= –y + 11
You Do it!
Find the difference using either the vertical or horizontal method.
a. (m – 3) – (–m + 12)
b. –2(c + 2.5) – 5(1.2c + 4)
Subtracting Linear
Expressions
Name: ______________________
Date: _______________________
Real-Life Application
The original price of a cowboy hat is d dollars. You use a coupon and buy the hat for (d – 2) dollars.
You decorate the hat and sell it for (2d – 4) dollars. Write an expression that represents your
earnings from buying and selling the hat. Interpret the expression.
earnings = selling price – purchase price
= (2d – 4) – (d – 2)
= (2d + (–4)) + (–d + 2)
= 2d + (–d) + (–4) + 2
= d + (–2) = d – 2
Use a model.
Write the difference.
Add the opposite.
Group like terms.
Combine like terms.
You earn (d – 2) dollars. You also paid (d – 2) dollars, so you doubled your money by selling the hat for
twice as much as you paid for it.
On your Own
What if in the example above, you sell the hat for (d + 2) dollars. How much do you earn from
buying and selling the hat?
earnings = selling price – purchase price
= (d + 2) – (d –2)
=d+2–d+2
=d–d+2+2
=4
You earn 4 dollars if you sell the hat for d + 2 dollars.