Simplify the following algebraic expression

Explanation

Strategy

First, we will remove the parentheses.  Then we will identify any like terms and combine them.

WHY

To simplify an expression we use properties of real numbers, such as the distributive property, to write an equivalent expression in simpler form.

Solution

Here, the distributive property is used both forward (to remove parentheses) and in reverse (to combine like terms)

• Replace the - symbol in front of (2x - 4) with -1
  • 4(x + 5) - 5 - (2x - 4) = 4(x + 5) - 5 - 1(2x - 4)
• Distribute the multiplication by 4 and -1
  • = 4x + 20 - 5 - 2x + 4
  • = 2x + 19

Think: (4 - 2x) = 2x
Think: (20 - 5 + 4) = 19