Solve the inequality l -6 + 4x l =< 7
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calendarEducator since 2010
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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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calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
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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