HOW TO ADD LINEAR EXPRESSIONS

A linear expression is a mathematical statement which contains a constant and variable or variables where the highest exponent of the variable is 1. If there is more than one variable, the variables must either be in addition or subtraction.

Examples of linear expressions :

3x + 2,

2x - y - 1

Example 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

Example 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

Example 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

Example 4 :

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

Solution :

= (s + t) + (2s - t) + (-s + t)

= s + t + 2s - t - s + t

Group the like terms.

= (s + 2s - s) + (t - t + t)

Combine the like terms.

= 2s + t

Example 5 :

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

Solution :

= (3a - 2b) + (2p + 3q)

= 3a - 2b + 2p + 3q

Example 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

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

Combine the like terms.

= 5a + (-5b) + 4

= 5a - 5b) + 4

Example 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

Example 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

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