Which of the following answers applies the distributive property of multiplication over addition correctly for simplifying 23 - 9(2x + 5) + 11x
The correct application of the distributive property of multiplication over addition is:
23 - 9(2x + 5) + 11x = 23 - 18x - 45 + 11x
To simplify the expression 23 - 9(2x + 5) + 11x using the distributive property of multiplication over addition correctly, follow these steps:
Step 1: Apply the distributive property to the term -9(2x + 5):
-9(2x + 5) = -18x - 45
Step 2: Substitute the simplified term -18x - 45 back into the expression:
23 - 18x - 45 + 11x
Step 3: Combine the like terms -18x and 11x:
-18x + 11x = -7x
Step 4: Combine the constant terms 23 and -45:
23 - 45 = -22
Step 5: Substitute the simplified terms -7x and -22 back into the expression:
-7x - 22
Therefore, the simplified expression is -7x - 22, which correctly applies the distributive property of multiplication over addition.
To apply the distributive property of multiplication over addition correctly for simplifying the expression 23 - 9(2x + 5) + 11x, you need to distribute the -9 to both terms inside the parentheses, and then combine like terms.
Here's the step-by-step process:
1. First, apply the distributive property to the expression -9(2x + 5):
-9 * 2x = -18x
-9 * 5 = -45
2. Rewrite the expression with the distributed terms:
23 - 18x - 45 + 11x
3. Combine like terms by adding or subtracting:
(-18x + 11x) + (23 - 45)
4. Simplify the expression further:
-7x + (-22)
The correct answer for the simplified expression using the distributive property is:
-7x - 22