There are x students in Mrs. Schwartz's third-grade class. One less than half the students have blue eyes. Six fewer children have green eyes than have blue eyes. The rest of the students have brown eyes. How many students have brown eyes?

a. 7
b. 8
c. (x/2)-7
d. x-7
e. x-8

please answer and explain

blue: x/2 - 1

green = blue-6

brown = x - blue - green
= x - (x/2 - 1) - ((x/2 - 1)-6)
= 8

x-(x/2+1)-[(x/2+1)-6]

Step 1: Distributive property
x-x/2-1-x/2-1-6
Step 2: Combine like terms
x-2x/2-8
x-x-8
0-8
Step 3: Solve
-8

Let's break down the information given step by step:

1. One less than half the students have blue eyes.
If we represent the number of students with blue eyes as "b," we can write this as:
b = (1/2)x - 1

2. Six fewer children have green eyes than have blue eyes.
If we represent the number of students with green eyes as "g," we can write this as:
g = b - 6

3. The rest of the students have brown eyes.
Since we know that the total number of students is "x," and we have accounted for the students with blue and green eyes, we can determine the number of students with brown eyes by subtracting the sum of students with blue and green eyes from the total number of students:
Number of students with brown eyes = x - (b + g)

Now, let's substitute the values from equations (1) and (2) into equation (3):

Number of students with brown eyes = x - (b + g)
Number of students with brown eyes = x - ((1/2)x - 1 + (b - 6))
Number of students with brown eyes = x - (1/2)x + 1 - b + 6

Next, let's substitute the value of "b" from equation (1) into the equation above:

Number of students with brown eyes = x - (1/2)x + 1 - ((1/2)x - 1) + 6
Number of students with brown eyes = x - (1/2)x + 1 - (1/2)x + 1 + 6
Number of students with brown eyes = x - x/2 + 1 - 1/2x + 1 + 6
Number of students with brown eyes = x - x/2 - 1/2x + 1 + 7

Now, let's simplify the expression:

Number of students with brown eyes = (2x - x)/2 - x/2 + 8
Number of students with brown eyes = x/2 + 8

Therefore, the number of students with brown eyes is x/2 + 8.

The answer is (e) x - 8.

To solve this problem, we need to break it down step by step.

First, let's consider the number of students who have blue eyes. We know that "one less than half the students" have blue eyes, so we can write this as:

Blue eyes = (1/2)x - 1

Next, we are told that "six fewer children have green eyes than have blue eyes." This means the number of students with green eyes is:

Green eyes = Blue eyes - 6
Green eyes = (1/2)x - 1 - 6

Finally, the remaining students have brown eyes. To calculate the number of students with brown eyes, we subtract the total number of students with blue and green eyes from the total number of students (x):

Brown eyes = x - (Blue eyes + Green eyes)

Now, let's substitute the expressions we derived earlier into the equation:

Brown eyes = x - [(1/2)x - 1 + (1/2)x - 1 -6]
Brown eyes = x - (x/2 - 2 - 6)
Brown eyes = x - (x/2 - 8)
Brown eyes = x - x/2 + 8
Brown eyes = (2x - x)/2 + 8
Brown eyes = x/2 + 8

So the number of students with brown eyes is x/2 + 8.

Now, let's see which answer choice matches our expression:

a. 7
b. 8
c. (x/2)-7
d. x-7
e. x-8

The correct answer is c. (x/2)-7.