Answer:
1. x = 4 and x = -1.
2. x = 17 and x = -7.
Explanation:
1.) |2x - 3| = 5
To solve this equation, we need to consider two cases: when 2x - 3 is positive and when it is negative.
Case 1: 2x - 3 ≥ 0
If 2x - 3 is positive, then we have:
2x - 3 = 5
Solving for x, we get:
x = 4
Case 2: 2x - 3 < 0
If 2x - 3 is negative, then we have:
-(2x - 3) = 5
Simplifying, we get:
-2x + 3 = 5
Solving for x, we get:
x = -1
Therefore, the solutions to the equation |2x - 3| = 5 are x = 4 and x = -1.
2.) |x - 5| = 12
To solve this equation, we again need to consider two cases: when x - 5 is positive and when it is negative.
Case 1: x - 5 ≥ 0
If x - 5 is positive, then we have:
x - 5 = 12
Solving for x, we get:
x = 17
Case 2: x - 5 < 0
If x - 5 is negative, then we have:
-(x - 5) = 12
Simplifying, we get:
-x + 5 = 12
Solving for x, we get:
x = -7
Therefore, the solutions to the equation |x - 5| = 12 are x = 17 and x = -7.