Question

Determine the solutions of the equation:

the absolute value quantity four thirds times x plus 2 end quantity minus 6 equals 0

x = 3 and x = 6
x = −3 and x = 6
x = −3 and x = 3
x = −6 and x = 3

Answer 1

To find the solutions of the equation, we need to isolate the absolute value expression and solve for x.

|4/3x + 2| - 6 = 0
|4/3x + 2| = 6

Now we split the equation into two cases since the absolute value can be positive or negative:

Case 1: 4/3x + 2 = 6
4/3x = 4
x = 3

Case 2: -(4/3x + 2) = 6
-4/3x - 2 = 6
-4/3x = 8
x = -6

Therefore, the solutions are x = 3 and x = -6.