Question

Solve and graph the solutions of the equation 2|x - 2| - 12 = 0.

Answer 1

To solve the equation 2|x - 2| - 12 = 0, we need to isolate the absolute value term.

Adding 12 to both sides, we get:
2|x - 2| = 12

Dividing both sides by 2, we have:
|x - 2| = 6

To solve for x, we will consider both the positive and negative cases.

Positive case:
If x - 2 is positive, then |x - 2| = x - 2. Thus, we have the equation:
x - 2 = 6

Adding 2 to both sides gives:
x = 8

Negative case:
If x - 2 is negative, then |x - 2| = -(x - 2) = -x + 2. Thus, we have the equation:
-x + 2 = 6

Subtracting 2 from both sides gives:
-x = 4

Multiplying both sides by -1, we have:
x = -4

Therefore, the solutions are x = 8 and x = -4.

To graph the solutions, we can draw a number line and plot the points x = 8 and x = -4 on it.

Number line:
---------- -4 ------ 8 ----------

Thus, the solutions are graphed on the number line.