How do you solve and graph #1/2<=c-3/4#?

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Answer 1 · 2017-12-19T16:55:46

See a solution process below:

Add #color(red)(3/4)# to each side of the inequality to solve for #c# while keeping the inequality balanced:

#1/2 + color(red)(3/4) <= c - 3/4 + color(red)(3/4)#

#(2/2 xx 1/2) + color(red)(3/4) <= c - 0#

#2/4 + color(red)(3/4) <= c#

#(2 + 3)/4 <= c#

#5/4 <= c#

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

#c >= 5/4#

To graph this we will draw a vertical line at #5/4# 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 >= 5/4 [-1, 3, -1, 1]}