How do you solve and graph #12<=t-9#?

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Answer 1 · 2017-11-27T21:36:38

See a solution process below:

First, add #color(red)(9)# to each side of the inequality to solve for #t# while keeping the inequality balanced:

#12 + color(red)(9) <= t - 9 + color(red)(9)#

#21 <= t - 0#

#21 <= t#

We can reverse or "flip" the entire inequality to state the solution in terms of #t#

#t >= 21#

To graph this we will draw a vertical line at #21# on the horizontal axis.

The line will be a solid line because the inequality operator contains an "or equal to" clause.

We will shade to the right side of the line because the inequality operator also contains a "greater than" clause:

graph{x >= 21 [-40, 40, -20, 20]}