ADDING LINEAR EXPRESSIONS WORKSHEET

Problem 1 :

Add (-6p - 8) and (-3p - 6)

Solution :

= (-6p - 8) + (-3p - 6)

= -6p - 8 - 3p - 6

Group the like terms.

= (-6p - 3p) + (-8 - 6)

Combine the like terms.

= (-9p) + (-14)

= -9p - 14

Problem 2 :

Add (-8r - 2) and (4r - 3).

Solution :

= (-8r - 2) + (4r - 3)

= -8r - 2 + 4r - 3

Group the like terms.

= (-8r + 4r) + (-2 - 3)

Combine the like terms.

= (-4r) + (-5)

= -4r - 5

Problem 3 :

Add (-z - 8) and (6z - 5).

Solution :

= (-z - 8) + (6z - 5)

 = -z - 8 + 6z - 5

Group the like terms.

= (-z + 6z) + (-8 - 5)

Combine the like terms.

= (5z) + (-13)

= 5z - 13

Problem 4 :

Add (s + t), (2s - t) and (-s + t).

Solution :

= (s + t) + (2s - t) +  (-s + t)

= s + 2s - s + t - t + t

Group the like terms.

= (s + 2s - s) + (t - t + t)

Combine the like terms.

= (2s) + (t)

= 2s + t

Problem 5 :

Add (3a - 2b) and (2p + 3q).

Solution :

= (3a - 2b) + (2p + 3q)

 = 3a - 2b + 2p + 3q

Problem 6 :

 Add (2a + 5b + 7), (8a - 3b + 3) and (-5a - 7b - 6).

Solution :

= (2a + 5b + 7) + (8a - 3b + 3) + (-5a - 7b - 6)

= 2a + 5b + 7 + 8a - 3b + 3 - 5a - 7b - 6

Group the like terms.

= (2a  + 8a - 5a) + (5b - 3b - 7b) + (7 + 3 - 6)

Combine the like terms.

= (5a) + (-5b) + (4)

= 5a - 5b + 4

Problem 7 :

Add (6x + 7y + 3), (-8x - y - 7) and (4x - 4y + 2).

Solution :

= (6x + 7y + 3)  + (- 8x - y - 7) + (4x - 4y + 2)

= 6x + 7y + 3 - 8x - y - 7 + 4x - 4y + 2

Group the like terms.

= (6x - 8x + 4x) + (7y - y - 4y) + (3 - 7 + 2)

Combine the like terms.

= (2x) + (2y) + (-2)

= 2x + 2y - 2

Problem 8 :

 Add (6a - 3b) and (7a - 5b).

Solution :

= (6a - 3b) + (7a - 5b)

= 6a - 3b + 7a - 5b

Group the like terms.

= (6a + 7a) + (-3b - 5b)

Combine the like terms.

= (13a) + (-8b)

= 13a - 8b

Problem 9 :

You start a new job. After w weeks, you have (10w + 120) dollars in your savings account and (45w + 25) dollars in your checking account. Write an expression that represents the total in both accounts. .

Solution :

initial amount in your savings account = 10w + 120

Amount in checking account = 45w + 25

Amount in total = 10w + 120 + 45w + 25

= 10w + 45w + 120 + 25

= 55w + 145

Problem 10 :

While catching fire flies, you and a friend decide to have a competition. After m minutes, you have (3m + 13) fire flies and your friend has (4m + 6) fire flies.

a. Write an expression that represents the number of fire flies you and your friend caught together.

b. The competition ends after 5 minutes. Who has more fire flies?

Solution :

a) total number of fire flies = 3m + 13 + 4m + 6

= 3m + 4m + 13 + 6

= 7m + 19

b) 

Number of fire flies caught up by you :

Number of minutes = 5

= 3m + 13

= 3(5) + 13

= 15 + 13

= 28

Number of fire flies caught up by a friend :

Number of minutes = 5

= 4m + 6

= 4(5) + 6

= 20 + 6

= 26

So, you caught more number of fire flies.

Problem 11 :

The expression 17n + 11 represents the perimeter (in feet) of the triangle. Write an expression that represents the measure of the third side.

Solution :

Perimeter of the triangle shown = 17n + 11

Sum of length of three sides = 17n + 11

5n + 6 + 4n + 5 + the length of third side = 17n + 11

(5n + 4n) + (6 + 5) + length of third side = 17n + 11

9n + 11 + length of third side = 17n + 11

length of third side = 17n + 11 - (9n + 11)

= (17n - 9n) + 11 - 11

= 8n

So, the length of the third side is 8n.

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