Using a graph tool
Let's proceed to analyze each case
case a) The equation[tex] |-x- 4| = 8 [/tex] will have two solutions
Is true
The solutions are
[tex] x=-12\\ x=4 [/tex]
see the attached figure N [tex] 1 [/tex]
case b) The equation [tex] 3.4|0.5x- 42.1| = -20.6 [/tex] will have one solution
Is False
The equation has no solution
The term [tex] 3.4|0.5x- 42.1| [/tex]
always will be positive
case c) Is not a equation
case d) The equation [tex] |2x- 10| = -20 [/tex] will have two solutions.
Is False
The equation has no solution
The term [tex] |2x- 10| [/tex]
always will be positive
case e) The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions.
Is True
The left side of the equation always will be greater than or equal to [tex] 4.6 [/tex]
case f) The equation = 5 will have infinitely many solutions.
Is not a equation
therefore
the answer is
case a) and case e) are true
