Question

Which equation has only one solution?

|x – 5| = –1
|–6 – 2x| = 8
|5x + 10| = 10
|–6x + 3| = 0

Answer 1

|–6x + 3| = 0

Explanation:

|x – 5| = –1

Absolute function cannot be equal to negative. so we cannot solve this absolute function

|–6 – 2x| = 8

For this absolute function we make two equations

-6-2x= 8 and -6-2x= 8. So we will get two solutions for x

|5x + 10| = 10

For this absolute function we make two equations

5x+10= 10 and 5x+10= -10. So we will get two solutions for x

|–6x + 3| = 0

For this absolute function we make two equations

-6x+3=0 and -6x+3=-0.

Both having same 0 on the right side. So we will get only one solutions for x

Answer 2

|–6x + 3| = 0

Explanation:

|x – 5| = –1

Has no solutions since an absolute value cannot be negative

|–6 – 2x| = 8

will have two solutions a positive and a negative

|5x + 10| = 10

will have two solutions a positive and a negative

|–6x + 3| = 0

will have only one solution because we cannot set zero to positive and negative values