which statement is true? the equation -3|2x + 1.2| = -1 has no solution. the equation 3.5|6x - 2| = 3.5 has…

Explanation:

Step1: Recall property of absolute - value

The absolute - value of a real number (y = |a|) is defined as (y=\begin{cases}a, & a\geq0\-a, & a < 0\end{cases}), and (|a|\geq0) for all real numbers (a).

Step2: Analyze the equation (-3|2x + 1.2|=-1)

First, rewrite it as (|2x + 1.2|=\frac{1}{3}). Since (\frac{1}{3}>0), we can solve (2x+1.2=\frac{1}{3}) and (2x + 1.2=-\frac{1}{3}), so it has two solutions.

Step3: Analyze the equation (3.5|6x - 2| = 3.5)

Rewrite it as (|6x - 2| = 1). Then we solve (6x-2 = 1) and (6x - 2=-1), so it has two solutions.

Step4: Analyze the equation (5|-3.1x + 6.9|=-3.5)

The left - hand side (5|-3.1x + 6.9|\geq0) (because (5>0) and (|-3.1x + 6.9|\geq0)), and the right - hand side (-3.5<0). So this equation has no solutions.

Step5: Analyze the equation (-0.3|3 + 8x|=0.9)

Rewrite it as (|3 + 8x|=- 3). Since the absolute - value of any real number is non - negative ((|3 + 8x|\geq0)) and (-3<0), this equation has no solution.

Answer:

The equation (-0.3|3 + 8x| = 0.9) has no solution.