|2t| - 5 = 7

Answer 1

To solve the equation, we'll isolate the absolute value by adding 5 to both sides:

|2t| = 7 + 5
|2t| = 12

Now, consider two cases:
Case 1: 2t = 12
If we remove the absolute value signs, we get 2t = 12. To solve for t, divide both sides by 2:
2t/2 = 12/2
t = 6

Case 2: -2t = 12
If we remove the absolute value signs and change the sign, we get -2t = 12. To solve for t, divide both sides by -2:
-2t/-2 = 12/-2
t = -6

Therefore, the solutions are t = 6 and t = -6.