To solve the inequality 2x - 7 > x + 5, we will isolate the variable x:

Step 1: Subtract x from both sides of the inequality
x - 7 > 5

Step 2: Add 7 to both sides of the inequality
x > 12

Thus, the inequality 2x - 7 > x + 5 is true for all values of x greater than 12, which corresponds to option B.

To solve the system of linear equations, we can either use the substitution method or the elimination method. In this case, we'll use the elimination method. Note that 2x + 3y = 6 (equation 1) and 4x - y = 5 (equation 2).

Step 1: Multiply equation 1 by 2 and add it to equation 2 to eliminate x:
4x + 6y = 12 (equation 1 multiplied by 2)
+
4x - y = 5 (equation 2)

Result: 5y = 17
Divide by 5:
y = 17/5

Step 2: Substitute the value of y in the first equation:
2x + 3(17/5) = 6
2x + 51/5 = 6
Multiply by 5 to eliminate fractions:
10x + 51 = 30
Subtract 51 from both sides:
10x = -21
Divide by 10:
x = -21/10

Thus, the solution to the system of linear equations is x = -21/10 and y = 17/5, which corresponds to option B.

To solve the system of linear equations, we can use either the substitution method or the elimination method. In this case, we'll use the elimination method since the second equation is already in the form of x - y.

Step 1: Add the two equations to eliminate y:
2x + y = 8
x - y = 4
--------------
3x = 12

Step 2: Divide by 3 to solve for x:
x = 4

Step 3: Substitute x into the first equation:
2(4) + y = 8
y = 8 - 8
y = 0

Thus, the solution to the system of linear equations is x = 4 and y = 0, which corresponds to option A.

To graph the system of linear inequalities y >= 2x - 1 and y <= x + 3, we first look at the equations y = 2x - 1 (option 1) and y = x + 3 (option 2). Then, test points to see which side of the equations satisfies the inequality. The inequality y >= 2x - 1 is true for points above the line y = 2x - 1 and the inequality y <= x + 3 is true for points below the line y = x + 3. Now, we must find the region where both inequalities are true (overlap). This will be the region below the line y = x + 3 and above the line y = 2x - 1. This corresponds to option A.

To find the inverse of a function, we swap the x and y coordinates (x and f(x), respectively) and then solve for the new f(x):

1. Replace f(x) with y:
y = 3x - 2

2. Swap x and y:
x = 3y - 2

3. Solve for y:
x + 2 = 3y
y = (x + 2) / 3

The inverse of the function f(x) = 3x - 2 is f^(-1)(x) = (x + 2) / 3, which corresponds to option C.