What is t if 5 + l 2t-12 l = 7
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,554 answers
starTop subjects are Math, Science, and Business
We have 5 + l 2t-12 l = 7.
Using the property that | 2t - 12| can be 2t - 12 and -(2t - 12) based on its value, we get :
5 + (2t - 12) = 7
=> 5 + 2t - 12 = 7
=> 2t = 7 - 5 + 12 = 14
=> t = 14/2
=> t = 7
Here we also see that 2*7 - 12 = 2 is positive.
Next we take 5 - (2t - 12) = 7
=> 5 - 2t + 12 = 7
=> -2t + 17 = 7
=> 2t = 10
=> t = 5
Here we also see that 2*t - 12 = -2 is negative.
So both t = 5 and t = 7 are valid results.
Therefore t = 5 and t = 7.
Related Questions
- 5/2t - t = 3 + 3/2t please solve
- 1 Educator Answer
- `f'(t) = 2t - 3sin(t), f(0) = 5` Find `f`.
- 1 Educator Answer
- If we know that sin(t) = 5/7 , how to find other identies like cos(t) and tan(t) ?
- 2 Educator Answers
- solve for x if l 2x -3 l < 5
- 1 Educator Answer
- How to find the integral of int(te^t, -e^(-2t), te^t(^2)) dt?
- 1 Educator Answer
calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
Given the equation:
5 + l 2t -12 l = 7
We need to find the value of t .
First we will isolate the absolute values by subtracting 5 from both sides.
==> l 2t -12 l = 7-5 = 2
==> l 2t -12 l = 2
Now we have 2 cases:
Case(1): Positive values.
==> 2t -12 = 2
==> 2t = 14
==> t= 7..........(1)
Case(2): Negative values.
==> -(2t-12) = 2
==> -2t +12 = 2
==> -2t = -10
==> t = -10/-2 = 5
==> t= 5.............(2)
From (1) and (2) , we conclude that the values of t are:
t = { 5, 7}
To find t in 5 + l 2t-12 l = 7.
We subtract 5 from both sides:
|2t-12| = 7- 5= 2.
Thereore if 2t -12> 0, then 2t-12 = 2.
=> 2t = 2+12 = 14.
t= 14/2 = 7.
If 2t-12 < 0, then 2t-12 = -2.
=> 2t = -2+12 = 10.
=> 2t = 10.
=> t = 10/2 = 5.
Therefore the 2 solutions of the equation are x = 7, or x = 5.
Student Answers