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[tex]\boxed{\{-5, 15\}}.[/tex]
[tex]|5 - x| - 10 = 0,[/tex]
[tex]|5 - x| = 10.[/tex]
The absolute value equation |A| = B can be rewritten as two separate equations:
[tex]1. \: 5 - x = 10 [/tex]
[tex]2. \: 5 - x = -10 [/tex]
Step 1: Solve the first equation
For the first equation:
[tex]5 - x = 10[/tex]
[tex]-x = 10 - 5[/tex]
[tex]-x = 5[/tex]
[tex]x = -5.[/tex]
Step 2: Solve the second equation
For the second equation:
[tex]5 - x = -10[/tex]
[tex]-x = -10 - 5[/tex]
[tex]-x = -15[/tex]
[tex]x = 15.[/tex]
The solution set of the equation |5 - x| - 10 = 0 is:
[tex]\{ -5, 15 \}.[/tex]