adding and subtracting linear expressions
Linear Expression - An algebraic expression in which the exponent of the variable is 1.
Examples: -4x 3X+5 5 - 1/6X
adding linear expressions
Like adding numbers, we can add linear expressions horizontally or vertically.
Horizontal Method
Change subtraction to addition using keep, change, change.
Eliminate parenthesis by using the distributive property.
Group like terms
Combine like terms ( don't forget to follow rules for adding integers!).
Example:
( -4y + 3 ) + ( 11y - 5 )
(-4y + 3) + (11y + -5)
-4y + 3 + 11y + -5
-4y + 11y + 3 + -5
7y + -2 OR 7y - 2
Vertical Method
Align like terms vertically
Use keep, change, change within algebraic expressions to change subtraction to addition
Add ( don't forget the rules for adding integers!).
(x - 2 ) + ( 3x + 8 )
( x - 2 )
+ ( 3x + 8)
2. ( x + -2)
+ ( 3x + 8)
3. 4x + 6
subtracting linear expressions
Like subtracting numbers, we can subtract linear expressions horizontally or vertically.
Horizontal method
Use keep change change within parenthesis to ensure that signs are correct
Use the distributive property to eliminate parenthesis
Group like terms
Combine like terms
Example
(7y + 5) - 2(4y - 3)
(7y + 5) - 2(4y + -3)
7y + 5 - 8y + 6
7y - 8y + 5 + 6
-y + 11
Vertical Method
Use keep change change to make sure that correct sign is used
Align terms vertically
Subtract
Example
(5x + 6) - (-x + 6)
( 5x + 6) + (x + 6)
5x + 6
+ x - 6
3. 6x