How do you solve #|7- 4x | > 10#?

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Answer 1 · 2018-05-02T12:56:53

The solution is #x in (-oo, -3/4] uu[17/4, +oo)#

This is an inequality with absolute values

#|7-4x| > 10#

#<=>#, #{(7-4x>10),(-7+4x>10):}#

#<=>#, #{(4x<7-10),(4x>10+7):}#

#<=>#, #{(x<-3/4),(x>17/4):}#

The solution is #x in (-oo, -3/4] uu[17/4, +oo)#

graph{(y-|7-4x|)(y-10)=0 [-11.69, 16.78, -0.24, 14]}

Answer 2 · 2018-05-02T13:06:51

Solution: # x < -3/4 or x > 17/4 #
In interval notation: #x in (-oo , -3/4) uu (17/4, oo)#

# |7-4 x| >10 or 7-4 x >10 or -4 x > 3 # or

#- x > 3/4 or x < -3/4 # OR

# |7-4 x| >10 or 7-4 x < -10 or -4 x < -17 # or

#- x < -17/4 or x > 17/4 #

Solution: # x < -3/4 or x > 17/4 #

In interval notation: #x in (-oo , -3/4) uu (17/4, oo)# [Ans]