Question

solve |x - 12| - 3 = 11.
-2, -26
4, -7
3, 25
-2, 26

Explanation:

Step1: Isolate the absolute value

Add 3 to both sides of the equation \(|x - 12| - 3 = 11\) to get \(|x - 12| = 11 + 3\).
So, \(|x - 12| = 14\).

Step2: Solve the absolute value equation

The absolute value equation \(|A| = B\) (where \(B\geq0\)) has solutions \(A = B\) or \(A = -B\).
For \(|x - 12| = 14\), we have two cases:

• Case 1: \(x - 12 = 14\)

Add 12 to both sides: \(x = 14 + 12 = 26\).

• Case 2: \(x - 12 = -14\)

Add 12 to both sides: \(x = -14 + 12 = -2\).

So the solutions are \(x = -2\) and \(x = 26\), which corresponds to the option \(-2, 26\).

Answer:

-2, 26