How do you solve # 3+ 5t < 3(t + 1)-4(2 - t)#?

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Answer 1 · 2017-05-27T22:39:23

Answer: #(4,oo)#

Solve #3+5t<3(t+1)-4(2-t)#

First, let us expand everything and combine like-terms on each side:
#3+5t<3t+3-8+4t#

#3+5t<7t-5#

Now, we can subtract #5t# and add #5# to both sides:
#3+5t-5t+5<7t-5-5t+5#

And simplify:
#8<2t#

Finally, we divide both sides by #2#:
#8/2<(2t)/2#
#4< t#
or
#t>4#

which we can also write in interval notation as #(4,oo)#