What is the expression 4+8(3x−2)−7x when simplified? Apply the order of operations and the commutative and distributive properties. Show all your work
To simplify the expression 4+8(3x−2)−7x, let's go step-by-step:
Step 1: Distributive Property
We need to distribute the 8 across the terms inside the parentheses:
4 + 8 * 3x - 8 * 2 - 7x
Step 2: Simplify within the parentheses
8 * 3x = 24x
8 * 2 = 16
So the expression becomes:
4 + 24x - 16 - 7x
Step 3: Combine like terms
Combine the x terms and the constant terms separately:
(24x - 7x) + (4 - 16)
This simplifies to:
17x - 12
Therefore, the simplified expression is 17x - 12.
To simplify the expression 4+8(3x−2)−7x, let's go step by step using the order of operations and the properties mentioned:
Step 1: Distributive property
Multiply 8 by each term inside the parentheses:
4 + 8 * 3x - 8 * 2 - 7x
Step 2: Simplify the multiplication
Multiply within each term:
4 + 24x - 16 - 7x
Step 3: Combine like terms
Combine the terms with the same variable:
(24x - 7x) + 4 - 16
Step 4: Simplify further
Subtract the coefficients of x: (24 - 7)x
Combine the constant terms: 4 - 16
Step 5: Final result
Simplify the expression:
17x - 12
So, the simplified form of the expression 4+8(3x−2)−7x is 17x - 12.
To simplify the expression, we will apply the distributive property and then use the order of operations (PEMDAS).
First, distribute the 8 to the terms inside the parentheses:
4 + 8 * 3x - 8 * 2 - 7x.
Next, simplify:
4 + 24x - 16 - 7x.
Now, combine like terms:
(24x - 7x) + (4 - 16),
17x - 12.
So, the simplified expression is 17x - 12.