Determine the roots of each equation algebraically. Make sure you do case 1 and case 2
|2x+1 |=9
Case 1: 2x + 1 = 9
Subtracting 1 from both sides: 2x = 8
Dividing both sides by 2: x = 4
Case 2: -(2x + 1) = 9
Multiplying both sides by -1: 2x + 1 = -9
Subtracting 1 from both sides: 2x = -10
Dividing both sides by 2: x = -5
Therefore, the roots of the equation |2x + 1| = 9 are x = 4 and x = -5.