Solve the inequality l -6 + 4x l =< 7

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The absolute value |x| is equal to x for all values of x >= 0 and -x for all values of x< 0.

We have l -6 + 4x l =< 7

As |x| is a positive value we have

-7=< (-6 + 4x) =< 7

=> -7 + 6=< -6 + 6 + 4x =< 7 + 6

=> -1 =< 4x =< 13

=> -1/4 =< x =< 13/4

Therefore x lies in [ -1/4 , 13/4]

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

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Given the inequality:

l -6 + 4x l =< 7

We need to find the values of x where the inequality holds.

We will rewrite the absolute values using the definition:

==> -7 =< (-6+4x) =< 7

Now we will add 6 to all sides.

==> 6-7 =< 4x =< 7+6

==> -1 =< 4x =<  13

Now we will divide by 4 all sides.

==> -1/4 =< x =< 13/4

Then we conclude that the values of x belongs to the interval [-1/4, 13/4]

==> x = [ -1/4  , 13/4]

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