|2t| − 5 = 7

Answer 1

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

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

Next, we can split the equation into two separate equations, one for when 2t is positive and one for when it is negative:

2t = 12 or 2t = -12

Solving for t in the first equation, we divide both sides by 2:

t = 12/2
t = 6

In the second equation, we again divide both sides by 2:

t = -12/2
t = -6

Therefore, the solutions to the equation |2t| - 5 = 7 are t = 6 and t = -6.