solve the inequality -3 -4 l 2x-7 l =< 9

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to solve -3 -4 l 2x-7 l =< 9.

I assume you mean -3 -4*( l 2x-7 l) =< 9

Now let's simplify the inequation

-3 -4*( l 2x-7 l) =< 9

=> -4*( l 2x-7 l) =< 12

=> ( l 2x-7 l) =< 12/-4

=> ( l 2x-7 l) => 3

As the absolute value |x| is -x for x< 0 and x for x>=0

=> 3=> (2x - 7)=> -3

3 => (2x - 7)

=> 10=> 2x

=> 5 => x

(2x - 7)=> -3

=> 2x => -3 + 7

=> 2x => 4

=> x=> 2

Therefore we have 5 => x => 2

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

Posted on

-3 - 4l2x-7l =< 9

First we will add 3 to both sides:

==> -4 l 2x -7 l =< 12

Now we will divide by -4 and reverse the inequality.

==> l 2x -7 l >= -3

Then, we have two cases,

==> -3 =< 2x -7 =< 3

Now we will add 7 to all sides:

==> 4 =< 2x =< 10

Now we will divide by 2:

==> 2 =< x =< 5

Then x values are between 2 and 5.

==> x belongs to the interval ( 2, 5).

==> x = ( 2, 5)

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