What is the expression 4 + 8 (3r - 2) - 7r when simplified? Apply the order of operations and the commutative and distributive properties. Show all your work.
To simplify the expression 4 + 8 (3r - 2) - 7r, we have to apply the order of operations and the commutative and distributive properties.
First, we simplify the expression inside the parentheses:
4 + 8 (3r - 2) - 7r
= 4 + 24r - 16 - 7r (distributive property)
= 24r - 7r + 4 - 16 (commutative property)
= (24r - 7r) + (4 - 16) (associative property)
= 17r - 12
Therefore, the simplified expression is 17r - 12.
To simplify the expression 4 + 8(3r - 2) - 7r, we need to apply the order of operations (PEMDAS) and the commutative and distributive properties. Let's break down the simplification step-by-step:
1. Distributive Property:
Apply the distributive property to multiply 8 with (3r - 2):
8 * 3r = 24r
8 * -2 = -16
The expression becomes: 4 + 24r - 16 - 7r
2. Commutative Property (Rearrange terms):
Rearrange the terms to bring similar terms together:
4 - 16 + 24r - 7r
The expression becomes: -12 + 17r
Therefore, the simplified expression is -12 + 17r.
To simplify the expression 4 + 8(3r - 2) - 7r, we will apply the order of operations, as well as the commutative and distributive properties.
Step 1: Commutative Property
Since addition is commutative, we can rearrange the terms to make the simplification process easier.
4 + (-7r) + 8(3r - 2)
Step 2: Distributive Property
Using the distributive property, we will multiply 8 with each term inside the parentheses.
4 + (-7r) + (8 * 3r) + (8 * -2)
Simplifying further,
4 + (-7r) + 24r - 16
Step 3: Combining like terms
Combine the like terms together to simplify the expression.
(-7r + 24r) + (4 - 16)
Simplifying further,
17r + (-12)
Step 4: Simplify further
Finally, combine the like terms and write the expression in a simplified form.
17r - 12
Therefore, the simplified expression is 17r - 12.