Adding & Subtracting Linear Expressions

A linear expression is an algebraic expression where the highest exponent on a variable is 1. Linear expressions are different from nonlinear expressions.

Adding and Subtracting Linear Expressions Examples

1. Ex: 1(x-2) + 1(3x + 8)
   So, 1x + 2 + 3x + 8
   Combine like terms: 1x + 3x - 2 + 8
   We get 4x + 6

2. (4-n) + 2(-5n+ 3)
   Combine like terms: 4 - n - 10n + 6
   We get -11n + 10

3. (-4y + 3) + (11y - 5)
   Combine like terms: -4y + 3 + 11y - 5
   We get 7y - 2

4. (-8z + 4) + (8z - 7)
   Combine like terms: -8z + 4 + 8z - 7
   We get -3

Simplifying Linear Expressions Examples

1. (5x + 6) - (-x + 6)
   Combine like terms: 5x + 6 + x - 6
   We get 6x

2. (7y+5) - 2(4y - 3)
   Combine like terms: 7y + 5 - 8y + 6
   We get -1y + 11

3. -2(c + 2.5) - 5(1.2c + 4)
   Combine like terms: -2c - 5 - 6c - 20
   We get -8c - 25

Earnings from Buying and Selling Linear Expressions

The original price of a cowboy hat is d dollars. If a coupon allows you to buy the hat for (d - 2) dollars and then you sell the hat after decorating it for (2d-4) dollars, your earnings from the transaction can be represented as (2d-4)-(d-2) = 2d + 4 - d + 2 = d - 2. This means you earn (2) dollars.

By selling the hat for twice the amount you paid for it, you double your money.