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

Answer:

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

Explanation:

Step1: Recall absolute - value property

The absolute - value of a number, $|a|$, is always non - negative, i.e., $|a|\geq0$ for all real numbers $a$.

Step2: Analyze the first equation

For $-3|2x + 1.2|=-1$, divide both sides by $-3$ to get $|2x + 1.2|=\frac{1}{3}$. Since $\frac{1}{3}>0$, this equation has two solutions.

Step3: Analyze the second equation

For $3.5|6x - 2| = 3.5$, divide both sides by $3.5$ to get $|6x - 2| = 1$. Since $1>0$, this equation has two solutions.

Step4: Analyze the third equation

For $5|-3.1x + 6.9|=-3.5$, divide both sides by $5$ to get $|-3.1x + 6.9|=-0.7$. But the absolute - value cannot be negative, so this equation has no solutions.

Step5: Analyze the fourth equation

For $-0.3|3 + 8x| = 0.9$, divide both sides by $-0.3$ to get $|3 + 8x|=-3$. Since the absolute - value of any real number is non - negative and $-3<0$, this equation has no solution.