what is the expression 4+8(3x-2)-7x when simplified? apply the order of operations and the commutative and distributive properties
To simplify the expression 4 + 8(3x - 2) - 7x, we'll follow the order of operations—often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right):
1. Parentheses
2. Exponents
3. Multiplication and Division
4. Addition and Subtraction
Let's go step by step:
First, we'll deal with the expression inside the parentheses and the multiplication by 8:
4 + 8(3x - 2) - 7x
Apply the distributive property to the term 8(3x - 2):
4 + 8 * 3x - 8 * 2 - 7x
4 + 24x - 16 - 7x
Notice that we multiplied 8 with both the terms inside the parentheses.
Next, we combine like terms (the constant terms 4 and -16, as well as the x-terms 24x and -7x):
(4 - 16) + (24x - 7x)
-12 + 17x
So the expression 4 + 8(3x - 2) - 7x when simplified is:
-12 + 17x
The order of terms doesn't matter because of the commutative property of addition, which means you could also write it as:
17x - 12
Both forms are equivalent.