Question

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.(4 points) Math Short Answer Rubric (4 points) Points Awarded Criteria 4 The answer is clear and correct. The answer shows that the student used problem-solving skills and reasoning. All work is shown or explained. 3 The answer is mostly correct. The student made small errors while solving. The answer shows that the student used some problem-solving skills and reasoning. Most work is shown or explained. 2 The answer is partially correct. The student made errors while solving. The answer shows that the student used some problem-solving skills or reasoning. Some work is shown or explained. 1 The answer is incorrect. The student made errors while solving. The answer shows little problem-solving skills or reasoning. Little or no work is shown. 0 The question is not answered.

Answer 1

To simplify the expression 4+8(3x−2)−7x, we will follow the order of operations and the distributive property.

First, we need to simplify the expression inside the parentheses: 3x−2.

Next, we will distribute the 8 to both terms inside the parentheses: 8(3x)−8(2).

This gives us: 24x−16.

Now, we can rewrite the entire expression as: 4+24x−16−7x.

Next, we can combine like terms by adding or subtracting the coefficients of x. In this case, we have 24x and -7x, so the expression becomes: 24x−7x.

This simplifies to: 17x.

Finally, we can combine the constants by adding or subtracting them. In this case, we have 4 and -16, so the expression becomes: 17x−12.

Therefore, the simplified expression is 17x−12.