How do you solve the equation? [absolute value(6t-9)]-21=0

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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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