solving linear inequalities by graphing: x-2y<=4

x=>1

I need help!!

For all x 1 and greater, and

y=>x/2 -2

To solve the system of linear inequalities x - 2y ≤ 4 and x ≥ 1 by graphing, follow these steps:

Step 1: Graph the first inequality x - 2y ≤ 4

To graph x - 2y ≤ 4, we first need to rewrite the inequality in slope-intercept form, which is y = mx + b. Let's isolate y:

x - 2y ≤ 4
-2y ≤ -x + 4
y ≥ (1/2)x - 2

Now, graph the line y = (1/2)x - 2.

- Start by plotting the y-intercept, which is at -2 on the y-axis (where x = 0).
- Then find another point on the line. To do this, choose any x-value and substitute it into the equation to solve for y. For example, when x = 2:
y = (1/2)(2) - 2
= 1 - 2
= -1
So, when x = 2, y = -1. Plot this point.

Connect the two points with a straight line. Since the inequality is y ≥ (1/2)x - 2, the line should be solid (not dashed) and shading should be above the line.

Step 2: Graph the second inequality x ≥ 1

This inequality is already in slope-intercept form, so it is easy to graph. We need to graph the line x = 1.

- Start by plotting the point (1, 0) on the x-axis.
- Draw a vertical line passing through (1, 0). Since the inequality is x ≥ 1, the line should be solid (not dashed) and shading should be to the right of the line.

Step 3: Determine the solution by finding the overlapping region

The solution to the system of inequalities is the region where both inequalities are true. Shade the region that is common to both shaded areas.

In this case, the solution is the shaded region above the line y = (1/2)x - 2 and to the right of the line x = 1. The shaded region should include the rightmost point of the line x = 1, but not the point itself.

I hope this helps! Let me know if you have any other questions.

To solve the system of linear inequalities, x - 2y <= 4 and x >= 1, we can graph both inequalities on a coordinate plane and find the region where the solution lies. Here's how you can do it step by step:

1. Start by graphing the first inequality, x - 2y <= 4:
a. Begin by treating the inequality as an equation, x - 2y = 4.
b. Rearrange the equation to slope-intercept form: y = (1/2)x - 2/2.
c. Plot a point on the y-axis at -1 (the y-intercept), and use the slope (1/2) to identify another point by moving up 1 unit and right 2 units.
d. Draw a dashed line through these two points to represent the inequality.

2. The inequality x >= 1 indicates that the x-coordinate must be greater than or equal to 1, which means we need to shade the region to the right of a vertical line passing through x = 1. Draw a solid vertical line at x = 1.

3. Now, you need to determine the overlapping region that satisfies both inequalities. Shade the area that is below or on the line from the first inequality (x - 2y <= 4) and to the right of the second inequality (x >= 1).

4. The shaded region represents the solution to the system of linear inequalities. Any point within this region will satisfy both inequalities.

Here is an image to help you visualize the solution:
![Graph of linear inequalities](https://i.imgur.com/CH5QnkB.png)

In this case, the shaded area below or on the line and to the right of x = 1 is the solution to the system of linear inequalities.