Adding linear expressions means, combining the like terms in the given expressions.

Here we can find some practice questions on adding linear expressions.

(1)  Add -6p - 8 and -3p - 6

(2)  Add -8r - 2 and 4r - 3

(3)  Add -z - 8 and 6z - 5

(4)  Add s + t,  2s - t, -s + t

(5)  Add 3a - 2b and 2p + 3q

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

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

(8)  Add (6a - 3b) and (7a - 5b)

## Adding linear expressions worksheet - Solution

Question 1 :

Add -6p - 8 and -3p - 6 using (i) horizontal (ii) Vertical method

Solution :

Horizontal method :

=  (-6p - 8) + (-3p - 6)

=  -6p - 8 - 3p - 6

=  -6p - 3p - 8 - 6

=  -9p - 14

Vertical method :

Hence -9p - 14 is the sum of the above linear expressions.

Question 2 :

Add -8r - 2 and 4r - 3 using (i) horizontal (ii) Vertical method

Solution :

Horizontal method :

=  (-8r - 2) + (4r - 3)

=  -8r - 2 + 4r - 3

=  -8r + 4r - 2 - 3

=  -4r -  1

Vertical method :

Hence -4r - 1 is the sum of the above linear expressions.

Question 3 :

Add -z - 8 and 6z - 5  using (i) horizontal (ii) Vertical method

Solution :

Horizontal method :

=  (-z - 8) + (6z - 5)

=  -z - 8 + 6z - 5

=  -z + 6z - 8 - 5

=  5z -  13

Vertical method :

Hence 5z - 13 is the sum of the above linear expressions.

Question 4 :

Add s + t,  2s - t, -s + t  using (i) horizontal (ii) Vertical method

Solution :

Horizontal method :

=  (s + t) + (2s - t) +  (-s + t)

=  s + 2s - s + t - t + t

=  2s + t

Vertical method :

Hence 2s + t is the sum of the above linear expressions.

Question 5 :

Add 3a - 2b and 2p + 3q

Solution :

=  (3a - 2b) + (2p + 3q)

=  3a - 2b + 2p + 3q

Hence 3a - 2b + 2p + 3q is the sum of the above linear expressions.

Question 6 :

Add 2a + 5b + 7, 8a - 3b + 3, - 5a - 7b - 6

Solution :

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

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

=  10a  - 5a + 5b - 10b + 10 - 6

=  5a - 5b + 4

Hence 5a - 5b + 4 is the sum of the above linear expressions.

Question 7 :

Add 6x + 7y + 3,- 8x - y - 7, 4x - 4y + 2

Solution :

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

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

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

=  10x - 8x + 7y - 5y + 5 - 7

=  2x + 2y - 2

Hence 2x + 2y - 2 is the sum of the above linear expressions.

Question 8 :

Add (6a - 3b) and (7a - 5b)

Solution :

=  (6a - 3b) + (7a - 5b)

=  6a - 3b + 7a - 5b

=  3a + 2b

Hence 3a + 2b is the sum of the above linear expressions.

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