Which equation has only one solution?
|x - 5| = - 1, |- 6 - 2x| = 8, |5x + 10| = 10, |- 6x + 3| = 0

Solution:

We will solve every absolute value equation to find out which equation has only one solution.

An absolute equation has two values of x.

Let us put the equation equal to both negative and positive values to solve the equation.

|x - 5| = - 1

⇒ x - 5 = 1 or x - 5 = -1

⇒ x = 6 or x = 4

Thus, the equation has two solutions.

|- 6 - 2x| = 8

⇒ - 6 - 2x = 8 or - 6 - 2x = - 8

⇒ 2x = - 14 or 2x =2 or x = 1.

Thus, the equation has two solutions.

|5x + 10| = 10

⇒ 5x + 10 = 10 or 5x + 10 = -10

⇒ 5x = 0 or 5x = - 20

⇒ x = 0 or x = - 20

Thus, the equation has two solutions.

|- 6x + 3| = 0

⇒ - 6x + 3 = 0 or - 6x + 3 = - 0

⇒ 6x = 3 or 6x = 3

⇒ x= 3/ 6 or 1/ 2

Thus, the equation |- 6x + 3| = 0 has only one solution.

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Which equation has only one solution?
|x - 5| = - 1, |- 6 - 2x| = 8, |5x + 10| = 10, |- 6x + 3| = 0

Summary:

The equation | - 6x + 3| = 0 has only one solution for x which satisfies the value of x = 1/ 2.