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 StartAbsoluteValue StartFraction one-half EndFraction x minus StartFraction 3 Over 4 EndFraction EndAbsoluteValue equals 0. = 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 StartAbsoluteValue StartFraction 1 Over 8 EndFraction x minus 1. EndAbsoluteValue equals 5. = 5 will have infinitely many solutions.

1. The equation |-x - 4| = 8 will have two solutions. (True)

5. The equation |0.5x - 0.75| + 4.6 = 0.25 will have no solutions. (True)

Step-by-step explanation:

1. The equation |-x - 4| = 8 will have two solutions. (True)

|-x - 4| = 8

-x - 4 = ±8

-x - 4 = 8 and - x - 4 = - 8

-x = 8 + 4 and - x = - 8 + 4

-x = 12 and - x = - 4

x = - 12 and x = 4

Therefore, it has two solutions x ∈ {-12, 4}

2. The equation 3.4|0.5x - 42.1| = - 20.6 will have one solution. (False)

Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.

3. The equation |1/2x - 3/4| = 0 will have no solutions. (False)

| (1/2) x - 3/4| = 0

(1/2) x - 3/4 = ±0

Since ±0 is the same

(1/2) x = 3/4

x = 2*3/4

x = 3/2

Therefore, it has one solution x = 3/2

4. The equation |2x - 10| = - 20 will have two solutions. (False)

Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.

5. The equation |0.5x - 0.75| + 4.6 = 0.25 will have no solutions. (True)

|0.5x - 0.75| + 4.6 = 0.25

|0.5x - 0.75| = 0.25 - 4.6

|0.5x - 0.75| = - 4.35

Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.

6. The equation | (1/8) x - 1| = 5 will have infinitely many solutions. (False)

| (1/8) x - 1| = 5

(1/8) x - 1 = ±5

(1/8) x - 1 = 5 and (1/8) x - 1 = - 5

(1/8) x = 5 + 1 and (1/8) x = - 5 + 1

(1/8) x = 6 and (1/8) x = - 4

x = 6*8 and x = - 4*8

x = 48 and x = - 32

Therefore, it has two solutions x ∈ {48, - 32}