Question

Which statements are true? Check all that apply.

The equation |–x – 4| = 8 will have two solutions.

The equation 3.4|0.5x – 42.1| = –20.6 will have one solution.

The equation = 0 will have no solutions.

The equation |2x – 10| = –20 will have two solutions.

The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions.

The equation = 5 will have infinitely many solutions.

Answer 1

Using a graph tool

Let's proceed to analyze each case

case a) The equation
`|-x- 4| = 8` will have two solutions

Is true

The solutions are

`x=-12\\ x=4`

see the attached figure N
`1`

case b) The equation
`3.4|0.5x- 42.1| = -20.6` will have one solution

Is False

The equation has no solution

The term
`3.4|0.5x- 42.1|`

always will be positive

case c) Is not a equation

case d) The equation
`|2x- 10| = -20` will have two solutions.

Is False

The equation has no solution

The term
`|2x- 10|`

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
`4.6`

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