How do you solve and graph #-23>=q-30#?

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Answer 1 · 2017-10-02T01:31:18

See a solution process below:

First, add #color(red)(30)# to each side of the inequality to solve for #q# while keeping the inequality balanced:

#-23 + color(red)(30) >= q - 30 + color(red)(30)#

#7 >= q - 0#

#7 >= q#

To state the solution in terms of #q# we can reverse or "flip" the entire inequality:

#q <= 7#

To graph this we will draw a vertical line at #7# 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 left side of the line because the inequality operator also contains a "less than" clause:

graph{x<= 7 [-10, 20, -7.50, 7.50]}