Question

Solve: 5. 6 = 3. 1 – 12. 5|1 – 0. 8x| 5. 6 = 3. 1 – 12. 5|1 – 0. 8x| 2. 5 = –12. 5|1 – 0. 8x| –0. 2 = |1 – 0. 8x| Finish the steps shown to find the possible value(s) for x that make the statement true. X = –1 or x = 1. 5 x = 1 or x = –1. 5 x = 0 There are no solutions.

Answer 1

The equation initially given has no solution since the absolute value cannot be equal to a negative number, which is the result after isolating the absolute value term.

Step-by-step explanation:

Let's continue solving the equation: 5.6 = 3.1 – 12.5|1 – 0.8x|. The next step after isolating the absolute value on one side of the equation is:

2.5 = – 12.5|1 – 0.8x|

Divide both sides by – 12.5:

–0.2 = |1 – 0.8x|

Since the absolute value is always non-negative, this equation has no solution because there is no value for x that will make |1 – 0.8x| equal to – 0.2. Absolute values can't be negative, thus we cannot proceed with steps to find x like we would for a non-negative result. In conclusion, according to the principles mentioned earlier, especially the fact that the absolute value of a real number cannot be negative, this equation has no solutions.

Answer 2

The possible values for x are; x = 1.5 and x = 1.

5.6 = 3.1 - 12.5 |1 - 0.8 x|

Subtract 3 .1 from both sides

2.5 = -12.5 |1 - 0.8x|

Divide both sides by -12.5

-0.2 = |1 - 0.8x|

Consider two cases

a. 1 - 0.8x = -0.2

b. 1 - 0.8x = 0.2

Solve each case case separately:

a. 1 - 0.8x = -0.2

Subtract 1 from both sides

-0.8x = -1.2

Divide by -0.8

x = 1.5

b. 1 - 0.8x = 0.2

Subtract 1 from both sides

-0.8x = -0.8

Divide by -0.8

x = 1

Therefore, the possible values for x are; x = 1.5 and x = 1.

The correct answer is: x = 1.5 or x = 1