Answer:
x = 20/3 or x = -12/5
Step-by-step explanation:
Solve for x over the real numbers:
2 abs(x - 1) = x/2 + 8
Divide both sides by 2:
abs(x - 1) = 1/2 (x/2 + 8)
Split the equation into two possible cases:
x - 1 = 1/2 (x/2 + 8) or x - 1 = 1/2 (-x/2 - 8)
Expand out terms of the right-hand side:
x - 1 = x/4 + 4 or x - 1 = 1/2 (-x/2 - 8)
Subtract x/4 - 1 from both sides:
(3 x)/4 = 5 or x - 1 = 1/2 (-x/2 - 8)
Multiply both sides by 4/3:
x = 20/3 or x - 1 = 1/2 (-x/2 - 8)
Expand out terms of the right-hand side:
x = 20/3 or x - 1 = -x/4 - 4
Add x/4 + 1 to both sides:
x = 20/3 or (5 x)/4 = -3
Multiply both sides by 4/5:
Answer: x = 20/3 or x = -12/5
