How do you solve the compound inequality #3t-7>=5# and #2t+6<=12#?

1 Answer

Answer:

There are no values of #t# that satisfy both inequalities.

Explanation:

We're looking for values of #t# that satisfy both expressions. So let's solve both and see what we get:

#3t-7ge5#

#3t-7color(red)(+7)ge5color(red)(+7)#

#3tge12#

#(3t)/color(red)(3)ge12/color(red)(3)#

#color(blue)(tge4#

#2t+6le12#

#2t+6color(red)(-6)le12color(red)(-6)#

#2tle6#

#(2t)/color(red)2le6/color(red)2#

#color(blue)(tle3#

Are there any values of #t# that satisfy both inequalities? No, and so therefore there are no solutions to this system of inequalities.