Question

find the values of x in this equation
10 + |2x - 12| - 14 = 0
-8 -6 -4 4 6 8 18
____ and ____

Explanation:

Step1: Simplify the equation

First, we simplify the given equation \(10 + |2x - 12| - 14 = 0\). Combine like terms: \(|2x - 12| - 4 = 0\), then we get \(|2x - 12| = 4\).

Step2: Solve the absolute - value equation

The absolute - value equation \(|A|=b\) (where \(b\geq0\)) is equivalent to \(A = b\) or \(A=-b\). Here, \(A = 2x - 12\) and \(b = 4\). So we have two cases:

Case 1: \(2x-12 = 4\)

Add 12 to both sides of the equation: \(2x=4 + 12\), so \(2x=16\). Divide both sides by 2: \(x = 8\).

Case 2: \(2x - 12=-4\)

Add 12 to both sides of the equation: \(2x=-4 + 12\), so \(2x = 8\). Divide both sides by 2: \(x = 4\).

Answer:

4 and 8