Question

Hiroto solved the equation 6 – 4|2x – 8| = –10 for one solution. His work is shown below. 6 – 4|2x – 8| = –10 –4|2x – 8| = –16 |2x – 8| = 4 2x – 8 = 4 2x = 12 x = 6 What is the other solution? –6 –4 2 10

Answer 1

Answer:

The solution set is

x = { 6 , 2 }

Step-by-step explanation:

Since we are given that

   6 – 4|2x – 8| = –10

⇒    – 4|2x – 8| = –10 -6 = -16

⇒    – 4|2x – 8| = -16

⇒         |2x – 8| = 4

by using definition of mode we get

                   2x – 8 = ± 4

either   2x – 8 = 4    or   2x – 8 = - 4

Case 1

  2x – 8 = 4

⇒      2x = 12

⇒        x = 6

Case 2

   2x – 8 = - 4

⇒       2x = - 4 + 8 = +4

⇒      2x  = 4

⇒         x = 2

Thus the solution set is

x = { 6 , 2 }