How do you solve #5v + 10<= - 4v - 17< 9- 2v#?

1 Answer

Answer:

#-13 < v <=- 3#

Explanation:

Break the inequality into 2 parts and solve each separately.

#color(blue)(5v +10 <= -4v -17) < 9-2v#
#5v +10 <= color(red)(-4v -17 < 9-2v)#

#color(blue)(5v +10 <= -4v -17)#
#color(blue)(10+17 <= -4v-5v)#
#color(blue)(27<=-9v)" "div -9" "larr# change sign around
#color(blue)(-3 >=v)#

#color(red)(-4v -17 < 9-2v)#
#color(red)(-17 -9 <-2v+4v)#
#color(red)(-26 <2v)#
#color(red)(-13 < v)#

Combine the two solutions for v:
#color(red)(-13 < v)" and "color(blue)(v<=-3)#

#color(red)(-13 <) v color(blue)(<= -3)#