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

2 Answers
smendyka
Jan 16, 2018

See a solution process below:

Explanation:

First, subtract #color(red)(1)# and #color(blue)(t)# from each side of the inequality to isolate the #t# term while keeping the inequality balanced:

#3t - color(blue)(t) + 1 - color(red)(1) < t - color(blue)(t) + 12 - color(red)(1)#

#3t - 1color(blue)(t) + 0 < 0 + 11#

#(3 - 1)color(blue)(t) < 11#

#2t < 11#

Now, divide each side of the inequality by #color(red)(2)# to solve for #t# while keeping the inequality balanced:

#(2t)/color(red)(2) < 11/color(red)(2)#

#(color(red)(cancel(color(black)(2)))t)/cancel(color(red)(2)) < 11/2#

#t < 11/2#

Megan
Jan 16, 2018

#t<11/2# or #t<5.5#

Explanation:

act as though the '<' sign is an equals '=' sign.
put all unknowns on the same side of the equation.
#3t+1-t<12#
simplify.
#2t+1<12#
minus any numbers that do not include the unknown.
#2t<11#
isolate the unknown.
#t<11/2# or #t<5.5#

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