How do you solve and graph abs(2c-1)<=7?

1 Answer
Jan 11, 2018

-3 \ le c \ le 4

Explanation:

| 2c-1 | \le7

Consider a general inequality with the absolute value:
| f(x) | \le a

By definition this is equivalent to solving the following inequalities:
f (x) \ le a and f (x) \ ge -a

In our specific case this means:
2c-1 \ le 7
2c-1 \ ge -7

So let's solve the first one:
2c-1 \ le 7
\ color (blue) {(1)} + 2c -1 \ le 7+ \ color (blue) {(1)}
2c \ le 8
\ frac {2} {2} c \ le \ frac {8} {2}
c \ le 4

Now the second:
2c-1 \ ge -7
2c \ ge -6
c \ ge -3

This is the graph of the first inequality:
graph{x <= 4 [-6.244, 6.243, -3.12, 3.123]}

And this of the second:
graph{x => - 3 [-4.163, 1.997, -1.455, 1.624]}

So the solution and the final graph are the common part of the two inequalities:
-3 \ le c \ le 4