Question

which statement is true?
the equation -3|2x + 1.2| = -1 has no solution.
the equation 3.5|6x - 2| = 3.5 has one solution.
the equation 5|-3.1x + 6.9| = -3.5 has two solutions.
the equation -0.3|3 + 8x| = 0.9 has no solution.

Explanation:

Step1: Recall absolute - value property

The absolute - value of a number \(|a|\geq0\) for all real numbers \(a\).

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

First, rewrite it as \(|2x + 1.2|=\frac{1}{3}\). Since \(\frac{1}{3}>0\), this equation has two solutions.

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

Rewrite it as \(|6x - 2| = 1\). This equation has two solutions (\(6x-2 = 1\) or \(6x - 2=-1\)).

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

Rewrite it as \(|-3.1x + 6.9|=-\frac{3.5}{5}=-0.7\). Since the absolute - value cannot be negative, this equation has no solution.

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

Rewrite it as \(|3 + 8x|=- 3\). Since the absolute - value cannot be negative, this equation has no solution.

Answer:

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