Final answer:
To distribute and then combine like terms for the expressions, apply the distributive property and gather like terms. Each expression is simplified by multiplying, adding, and subtracting correctly to consolidate x terms and constants. The results are 7x + 28, 11x - 10, 28 - 17x, and 3x - 3 respectively.
The correct answer is D. 7 - 5x - 2(-4x + 5)
Step-by-step explanation:
To distribute and then combine like terms for the given expressions, we will apply the distributive property A(B+C) = AB + AC and then gather like terms. Here is how we can simplify each expression:
A. 4(3x + 7) - 5x: First, distribute 4 to each term inside the parentheses: 4*3x + 4*7. Then, simplify and subtract 5x: 12x + 28 - 5x. Now, combine like terms: (12x - 5x) + 28 = 7x + 28.
B. -2(-4x + 5) + 3x: Distribute -2 across the parentheses: -2*(-4x) + -2*5. Then, simplify and add 3x: 8x - 10 + 3x. Combine like terms: (8x + 3x) - 10 = 11x - 10.
C. 3x + 4(7 - 5x): Distribute 4: 3x + 4*7 - 4*5x. Simplify: 3x + 28 - 20x. Combine like terms: 28 - (20x - 3x) = 28 - 17x.
D. 7 - 5x - 2(-4x + 5): Distribute -2: 7 - 5x - -2*4x + -2*5. Simplify: 7 - 5x + 8x - 10. Combine like terms: (8x -5x) + (7 - 10) = 3x - 3.
Lastly, we eliminate terms wherever possible to simplify the algebra and check the answer to see if it is reasonable.
The correct answer is D. 7 - 5x - 2(-4x + 5)