Question

6 ) solve and graph the inequality |2x - 4| = -12
isolate the absolute value expression
empty box
empty box
or
set up two inequalities to solve
empty box empty box
empty box empty box
answer empty box
number line with red arrow, three tick marks with empty boxes, and purple arrows/circles

Explanation:

Step1: Recall absolute value property

The absolute value of a number, denoted as \(|a|\), is always non - negative, i.e., \(|a|\geq0\) for any real number \(a\). In the equation \(|2x - 4|=- 12\), the left - hand side \(|2x - 4|\) represents the absolute value of the expression \(2x-4\), so \(|2x - 4|\geq0\) for all real values of \(x\). But the right - hand side of the equation is \(-12\), which is negative.

Step2: Determine the solution

Since the absolute value of a number cannot be negative, there is no real number \(x\) that satisfies the equation \(|2x - 4|=-12\).

Answer:

No solution (or \(\varnothing\))