How do you solve the inequality #3t + 1 < t + 12#?

2 Answers
Jacobi J.
Jun 2, 2018

#t<11/2#

Explanation:

The key realization here is that, for the most part, we can treat this like an equation. If we had

#3t+1=t+12#

we would subtract #1# from both sides, and subtract #t#. We can do the same thing with #3t+1<t+12#. We get

#3t< t+11#

#=>2t<11#

Dividing both sides by #2#, we get

#t<11/2#

Hope this helps!

Jim G.
Jun 2, 2018

#t<11/2#

Explanation:

#"collect terms in t on the left side and numeric values on"#
#"the right side"#

#"subtract "t" from both sides"#

#3t-t+1< cancel(t)cancel(-t)+12#

#2t+1< 12#

#"subtract 1 from both sides"#

#2t<11#

#"divide both sides by 2"#

#t<11/2" is the solution"#

#t in(-oo,11/2)larrcolor(blue)"in interval notation"#

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