Answer:
B. |3x - 6| + 17 > 15
C. |5x - 4| > -8
Step-by-step explanation:
The absolute value of a number is its positive numerical value.
To determine which absolute value inequalities have all real solutions, isolate the absolute value on one side of the equation.
Option A
|5x - 7| < -2
No solutions, as an absolute value cannot be less than zero.
Option B
|3x - 6| + 17 > 15
⇒ |3x - 6| + 17 - 17 > 15 - 17
⇒ |3x - 6| > -2
True for all values of x, as an absolute value is always positive and therefore will always be greater than -2.
Option C
|5x - 4| > -8
True for all values of x, as an absolute value is always positive and therefore will always be greater than -8.
Option D
-2|3x - 5 | > 3
Divide both sides by -2 (remembering to flip the inequality sign):
⇒ |3x - 5| < -³/₂
No solutions, as an absolute value cannot be less than zero.
