Describe two methods for adding or subtracting linear expressions.

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

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