Question

85 POINTS NEED ANSWER ASAP

a. A student was trying to solve the absolute value equation 8-|3x+2|=4 but is not sure whether they made a mistake. Her work is shown below:


Review her work to determine whether she made a mistake. Did she make a mistake? If so, please circle the mistake and explain why it is incorrect.



b. If you found an error in part a, please solve the equation 8-|3x+2|=4 correctly and show all work.

Answer 1

She was wrong all along

In the first step ,

She added 8 to the both sides but it should have been the other way round i.e. she were supposed to deduct 8 from both side.

• 8 -|3x + 2| - 8 = 4 -8
• - | 3x + 2 | = -4
• |3x + 2| = 4

Now, we'll split the equation into two parts i.e one positive and the other negative,

+ve :

• 3x + 2 = 4
• 3x = 2
• x = 2/3

-ve :

• 3x - 2 = 4
• 3x = 6
• x = 6/3
• x = 2

Thus, x = 2 and 2/3.