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Solve the inequality and graph the solution.

20>5c
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

1 answer

To solve the inequality \( 20 > 5c \), we start by isolating \( c \).

  1. Divide both sides by 5: \[ \frac{20}{5} > c \] This simplifies to: \[ 4 > c \] or \[ c < 4 \]

The solution to the inequality is \( c < 4 \).

Graphing the Solution

  1. Endpoints: The endpoint is 4.
  2. Type of Endpoint: Since \( c < 4 \) does not include 4, we make it an open endpoint (represented as an empty circle).
  3. Direction: The solution includes all values less than 4, which means we will shade to the left.

Graph Representation

  • Draw a number line.
  • Place an open circle at 4 (indicating that 4 is not included).
  • Shade everything to the left of 4.

Here’s a visual representation of the graph:

-----|-----|-----|-----|-----|-----|-----|-----|-----|----->
   -2    -1     0     1     2     3    (4)    5     6    
                           o
<--------------------------

In this graph:

  • The open circle at 4 denotes that it is not part of the solution set.
  • The shaded area to the left indicates all values of \( c \) that satisfy the inequality \( c < 4 \).