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.

The True statements are:

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

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

We have Statements:

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

So, it has two solutions.

The second statement is:

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

As we can see that the right side of the equation has a negative value.

so, this equation has no solution.

The third statement is:

3. The equation will have no solutions.  

So, it has one solution.

The fourth statement is:

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

As the right side of the equation has a negative value.

So, it has no solution.

The fifth statement is:

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

|0.5x – 0.75| + 4.6 = 0.25

|0.5x – 0.75| = 0.25 - 4.6

|0.5x – 0.75| = -4.35

As the right side of the equation has a negative value.

So, it has no solution.

The sixth statement is:

6. The equation will have infinitely many solutions.

So, it has two solutions.

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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}

step-by-step explanation:

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