**Adding linear expressions worksheet :**

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)

**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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