Final answer:
To determine which statement is true, we solve each equation and find the number of solutions. The correct statement is B, as the equation 3.5|6x - 2| = 3.5 has one solution.
Step-by-step explanation:
In order to determine which statement is true, we need to solve each equation and see if they have any solutions.
A. The equation –3|2x + 1.2| = –1 can be rewritten as 2x + 1.2 = -1/3. Solving for x, we get x = -1.2/2, which is a solution. Therefore, statement A is false.
B. The equation 3.5|6x – 2| = 3.5 can be simplified to |6x - 2| = 1. Dividing both sides by 3.5, we get |6x - 2| = 1/3. This equation has one solution, x = 1/3. Therefore, statement B is true.
C. The equation 5|–3.1x + 6.9| = –3.5 is not possible. The absolute value is always non-negative, so the left side of the equation can never equal a negative number. Therefore, statement C is false.
D. The equation –0.3|3 + 8x| = 0.9 can be simplified to |3 + 8x| = 3. Solving for x, we get x = -3/8, which is a solution. Therefore, statement D is false.
Based on our calculations, the correct statement is B. The equation 3.5|6x – 2| = 3.5 has one solution.