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

1 Answer
Jan 11, 2018

Answer:

# -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 #