How do you solve the inequality #-4z-7<9 #?

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Answer 1 · 2018-07-21T21:45:25

#z > -4#

#-4z - 7 < 9#

Add #color(blue)(4z)# to both sides:
#-4z - 7 quadcolor(blue)(+quad4z) < 9 quadcolor(blue)(+quad4z)#

#-7 < 9 + 4z#

Subtract #color(blue)9# from both sides:
#-7 quadcolor(blue)(-quad9) < 9 + 4z quadcolor(blue)(-quad9)#

#-16 < 4z#

Divide both sides by #color(blue)4#:
#(-16)/color(blue)4 < (4z)/color(blue)4#

#-4 < z#

Therefore,
#z > -4#

Hope this helps!

Answer 2 · 2018-07-21T23:08:19

#z> -4#

Our end goal is to isolate #z#, so let's start by adding #7# to both sides. We're left with

#-4z<16#

Next, to isolate #z# further, let's divide both sides by #-4#. Recall that when we apply a negative to an inequality, the sign flips.

We now have

#z> -4#

Hope this helps!