Answer:
a
Step-by-step explanation:
Given
2| x - 3 | + 5 = 17 ( subtract 5 from both sides )
2| x - 3 | = 12 ( divide both sides by 2 )
| x - 3 | = 6
The absolute value function always returns a positive value but the expression inside can be positive or negative, that is
x - 3 = 6 OR -( x - 3) = 6
x - 3 = 6 ( add 3 to both sides )
x = 9
OR
-( x - 3) = 6 ← distribute left side
- x + 3 = 6 ( subtract 3 from both sides )
- x = 3 ( multiply both sides by - 1 )
x = - 3
As a check
Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.
x = 9 → 2|9 - 3| + 5 = 2|6| + 5 = (2 × 6) + 5 = 12 + 5 = 17 ← True
x = - 3 → 2|- 3 - 3| + 5 = 2| - 6 | + 5 = (2 × 6) + 5 = 12 + 5 = 17 ← True
Hence x = 9 or x = - 3 are the solutions → a
