Addition of Algebraic Expressions

Example 1:

$$ \textup{Find the sum of} \; 3x \; \textup{and} \; 4x$$

Solution:

$$ 3x + 4x = 7x$$

Example 2:

$$ \textup{Find the sum of} \; 7a \; \textup{and} \; 5a$$

Solution:

$$ 7a + 5a = 12a$$

Example 3:

$$ \textup{Find the sum of} \; 5x \; \textup{and} \; -2x$$

Solution:

$$ 5x + (-2x) = 5x - 2x = 3x$$

Example 4:

$$ \textup{Find the sum of} \; 8x \; \textup{and} \; x$$

Solution:

$$ 8x + x = 9x$$

Example 5:

$$ \textup{Find the sum of} \; 4a, \; a \; \textup{and} \; 10a$$

Solution:

$$ 4a+a+10a=15a$$

Example 6:

$$ \textup{Find the sum of} \, -3c, \, -5c, \, -2c \, \textup{and} \, -8c$$

Solution:

$$ (-3c)+(-5c)+(-2c)+(-8c) $$ $$ =-3c-5c-2c-8c $$ $$ =-18c $$

Example 7:

$$ \textup{Simplify} \; 3x+2y+7x+5y $$

Solution:

$$ 3x+2y+7x+5y $$ $$ =3x+7x+2y+5y $$ $$ =10x+7y $$

Example 8:

$$ \textup{Simplify} \; 8x+9+4x+15$$

Solution:

$$ 8x+9+4x+15 $$ $$ =8x+4x+9+15 $$ $$ =12x+24 $$

Example 9:

Simplify

$$ 3a+2b+4c+4a+3b+c+5a+b+8c$$

Solution:

$$ 3a+2b+4c+4a+3b+c+5a+b+8c $$ $$ =3a+4a+5a+2b+3b+b+4c+c+8c$$ $$ =12a+6b+13c$$

Example 10:

$$ \textup{Find the sum of} \; 12a+7b \; \textup{and} \; 6a+9b$$

Solution:

$$ (12a+7b)+(6a+9b)$$ $$ =12a+7b+6a+9b$$ $$ =12a+6a+7b+9b$$ $$ =18a+16b$$