How do you solve the equation? [absolute value(6t-9)]-21=0
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We have to solve the equation |6t - 9| - 21 =0
|6t - 9| - 21 =0
=> |6t - 9| = 21
This gives us two equations
6t - 9 = 21
=> 6t = 21 + 9
=> 6t = 30
=> t = 30/6
=> t = 5
And 9 - 6t = 21
=> -6t = 21 - 9
=> -6t = 12
=> t = 12/-6
=> t = -2
Therefore we have t = -2 and t = 5
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When you solve an equation that contains absolute value, you'll have to consider 2 cases.
First, we'll re-write the equation using mathematical symbol for absolute value:
|6t-9| - 21 = 0
Now, we'll add 21 both sides:
|6t-9| = 21
We'll factorize by 3 to the left side:
|3(2t - 3)| = 21
3|2t - 3| = 21
We'll divide by 3:
|2t - 3| = 7
We'll discuss 2 cases:
2t-3 for 2t-3>=0
2t>=3
t>=3/2
-2t + 3 for 2t-3<0
2t<3
t<3/2
Case 1: t belongs to the interval [3/2, +infinite).
2t - 3 = 7
2t = 10
t = 5
Since t = 5 belongs to the range [3/2, +infinite), we'll accept it as solution.
Case 2: t belongs to the interval (infinite,3/2).
-2t + 3 = 7
-2t = 4
t = -2
Since t = -2 belongs to the range (infinite,3/2), we'll accept it as solution.
The solutions of the given equation are: {-2 ; 5}.
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