3 l x-3 l + 4 = 10  find x.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to solve 3 l x-3 l + 4 = 10.

3 l x-3 l + 4 = 10

=> 3* |x - 3| = 6

=> | x -3 | = 2

This equation is satisfied for the following cases:

x - 3 = 2

=> x  = 5

and 3 - x = 2

=> x = 1

Therefore x is equal to 5 and 1.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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3 l x-3 l  + 4 = 10

To solve for x , we need to isolate the absolute value on the left side.

First we will subtract 4 from both sides.

==> 3 l x-3 l = 6

Now we will divide by 3.

==> l x-3 l = 2

Now we have two cases.

Case(1): Positive value.

==> x-3 = 2  ==> x = 5

Case(2) : negative value.

==> -(x-3) = 2 ==> -x + 3 = 2 ==> -x = -1 ==> x = 1

==> Then the values of x are :

x = { 1, 5}

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neela | High School Teacher | (Level 3) Valedictorian

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Q: 3 l x-3 l + 4 = 10  We have to find x.

Solution:

We  subtract 4 from both sides of the equation:

 3 |x-3| = 10-4 =6.

 3|x-3| = 6.

We divide both sides of 3|x-3| = 6, by 3:

 |x-3| = 2.

If x> 3,  then |x-3| = x-3  = 2 .

So x- 3 = 2, Or x = 5.

If x< 3, then  |x-3| = 3-x = 2.

So 3-2 = x. Or x= 1.

So x= 1, or x = 5.

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