Question

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

Answer 1

See a solution process below:

Explanation:

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: