Answer:
f(x) = 2x + 6, x < - 1/5
-8x + 4, -1/5 ≤ x ≤ 5/3
-2x - 6, x>5/3
Step-by-step explanation:
3x-5 ≥ 0, 5x + 1 ≥ 0
3x ≥ 5, 5x ≥ -1
x ≥ 5/3, x ≥ -1/5
Intervals: x < -1/5, -1/5 ≤ x ≤ 5/3, x>5/3
Equations:
-(3x - 5) + (5x + 1) = -3x + 5 + 5x + 1 = 2x + 6
-(3x - 5) -(5x + 1) = -3x + 5 - 5x - 1 = -8x + 4
3x - 5 -(5x + 1) = 3x - 5 - 5x - 1 = -2x - 6
Piecewise Function:
f(x) = 2x + 6, x < - 1/5
-8x + 4, -1/5 ≤ x ≤ 5/3
-2x - 6, x>5/3
Here is your graph (and the piecewise functions to the right):
