How do you solve and graph #-3

Question

How do you solve and graph #-3<=7c+4<18#?

Julia Adams · Accepted Answer

See a solution process below:

First, subtract #color(red)(4)# from each segment of the system of inequalities to isolate the #c# term while keeping the system balanced:

#-3 - color(red)(4) <= 7c + 4 - color(red)(4) < 18 - color(red)(4)#

#-7 <= 7c + 0 < 14#

#-7 <= 7c < 14#

Now, divide each segment by #color(red)(7)# to solve for #c# while keeping the system balanced:

#-7/color(red)(7) <= (7c)/color(red)(7) < 14/color(red)(7)#

#-1 <= (color(red)(cancel(color(black)(7)))c)/cancel(color(red)(7)) < 2#

#-1 <= c < 2#

Or

#c >= -1# and #c < 2#

Or, in interval notation:

#[-1, 2)#

To graph this we will draw vertical lines at #-1# and #2# on the horizontal axis.

The line at #-1# will be a solid line because the inequality operator contains an "or equal to" clause. The line at #2# will be a dashed line because the inequality operator does not contain an "or equal to" clause.

We will shade between the lines to show the interval:

Jace Anderson · Answer

undefined To solve and graph the compound inequality -3 ≤ 7c + 4 < 18:

1. Subtract 4 from all parts of the compound inequality:
   -3 - 4 ≤ 7c + 4 - 4 < 18 - 4
   -7 ≤ 7c < 14

2. Divide all parts of the compound inequality by 7:
   -7/7 ≤ 7c/7 < 14/7
   -1 ≤ c < 2

3. The solution for c is -1 ≤ c < 2.

4. To graph this solution on a number line, plot a closed circle at -1 and an open circle at 2. Then shade the area between -1 and 2 to represent the interval where -1 ≤ c < 2.

How do you solve and graph #-3&lt;=7c+4&lt;18#?

How do you solve and graph #-3<=7c+4<18#?