Question

what is the solution to 3|−3x + 9| = −18?
○ x = −5
○ x = 5 or x = 1
○ x = −5 or x = 1
○ no solution

Explanation:

Step1: Analyze the absolute value equation

The equation is \(3|-3x + 9|=-18\). First, divide both sides by 3 to simplify.
\(\frac{3|-3x + 9|}{3}=\frac{-18}{3}\)
Which simplifies to \(|-3x + 9|=-6\).

Step2: Recall the property of absolute value

The absolute value of a number, denoted as \(|a|\), is always non - negative, i.e., \(|a|\geq0\) for any real number \(a\). In our equation, the left - hand side is \(|-3x + 9|\), which represents the absolute value of \(-3x + 9\). So, \(|-3x+9|\geq0\) for all real values of \(x\). But the right - hand side of the equation \(|-3x + 9|=-6\) is \(-6\), and \(-6<0\). Since a non - negative number can never be equal to a negative number, there are no real values of \(x\) that satisfy the equation.

Answer:

no solution