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.

Answer 1

Only the fourth statement is true.

Quick checks:
- –3|2x + 1.2| = –1 → |2x+1.2| = 1/3 (positive) → two solutions. (False)
- 3.5|6x – 2| = 3.5 → |6x–2| = 1 → two solutions (x = 1/6, 1/2). (False)
- 5|–3.1x + 6.9| = –3.5 → |…| = –0.7 (impossible) → no solution. (False)
- –0.3|3 + 8x| = 0.9 → |3+8x| = 0.9/(-0.3) = −3 (impossible) → no solution. (True)