To find the x-intercept of the linear equation 2x - 4y = 12, set y = 0 and solve for x:

2x - 4(0) = 12
2x = 12
x = 6

Thus, the x-intercept is x = 6, which corresponds to option C.

To find the value of f(3), substitute x = 3 into the function f(x):

f(3) = 2(3)² - 6(3) + 5
f(3) = 2(9) - 18 + 5
f(3) = 18 - 18 + 5
f(3) = 0 + 5
f(3) = 5

Thus, the value of f(3) is 5, which corresponds to option A.

To solve the inequality 5 - 3x < 8, we will isolate the variable x: Step 1: Subtract 5 from both sides of the inequality -3x < 3 Step 2: Divide by -3 (and reverse the inequality direction since we're dividing by a negative number) x > -1

Thus, the inequality 5 - 3x < 8 is true for all values of x greater than -1, which corresponds to option B.

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 solve the absolute value equation |3x - 4| = 8, we need to split the equation into two separate equations:

3x - 4 = 8 and 3x - 4 = -8

For the first equation, add 4 to both sides:
3x = 12
Divide by 3:
x = 4

For the second equation, add 4 to both sides:
3x = -4
Divide by 3:
x = -4/3

Thus, the solution to the absolute value equation |3x - 4| = 8 is x = 4 and x = -4/3, which corresponds to option D.