How do you solve compound inequalities #5a-4>16 or 3a + 2 <17#?

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Answer 1 · 2018-07-21T16:00:48

#a>4# or #a<5#

We have the following:

#color(limegreen)(5a-4>16)# and #color(blue)(3a+2<17)#

Let's start with our green inequality. We can add #4# to both sides to get

#color(limegreen)(5a>20)#

Next, divide both sides by #5# to get

#color(limegreen)(a>4)#

Next, let's look at our blue inequality. Let's subtract #2# from both sides to get

#color(blue)(3a<15)#

Lastly, let's divide bot hsides by #3# to get

#color(blue)(a<5)#

Our solutions are

#a>4# or #a<5#

Hope this helps!

Answer 2 · 2018-07-21T16:28:23

#a>4# or #a<5#

1) Solving first inequality:

#5a-4>16#

#5a-4+4>16+4#

#5a>20#

#{5a}/5>20/5#

#a>4#

2) Solving second inequality:

#3a+2<17#

#3a+2-2<17-2#

#3a<15#

#{3a}/3<15/3#

#a<5#