I do not understand how to figure out my problem below and can not find an example in my book. Can someone give me a suggestion on how I can arrive at my answer.

Problem:

Write a system of inequalities whose solution set is the region shown.

graph

Hard to say without seeing the graph.

If for example the domain between -4 and + 4 is shown with big black dots at the end, then your answer would be :
|x|</=4
or
-4 </= x </= +4
If it was from -5 to +7 then:
-5</= x </= +7
If it is outside the domain from -4 to +4 (to the left of -4 and to the right of +4 ) then
|x|>4
etc etc etc

I need to do the shaded area which starts at (3,-1) and continues to expand negatively. (3,1) is the start(like the start of a neck tie) and expands to the end of the tie growing each section.

I have

one line on the y axis runs through (0,5), slope down 2 over 1. Other line goes through y axis at (0,2) or on x axis at (2,0) with slope down 2 over 3.

i am in the 5th grade my question is write each number in two other forms, 10+ 4+ 0.05

To write a system of inequalities that represents the given region, you will need to analyze the graph and determine the boundaries of the region.

Here's a step-by-step approach to arrive at your answer:

1. Study the graph: Examine the region carefully to identify the boundaries, including the lines and curves.

2. Identify the equations of the lines: Determine the equations of the lines that form the boundary of the region. You may need to find the slope-intercept form (y = mx + b) or the standard form (Ax + By = C) for each line based on the information provided.

3. Determine the inequalities: Based on the direction and relationship of each line to the region, write the appropriate inequalities to represent the boundary. You will need to identify whether the region includes the lines themselves (using ≤ or ≥) or if it is strictly within the region (using < or >).

4. Combine the inequalities: Write down the final system of inequalities by combining all the inequalities.

5. Check: Double-check the system of inequalities and ensure it accurately represents the given region. You can also test points within and outside the region to verify if they satisfy the inequalities.

By following these steps, you should be able to construct a system of inequalities that represents the given region. Remember, it's essential to understand the boundaries and relationships within the graph to construct an accurate system.