Which graph shows the solution to the inequality?
x - 4 ≤ -1
The solution to the inequality x - 4 ≤ -1 is x ≤ 3.
The graph that shows this solution is:
<graph style="width:400px;height:300px" graph_src="https://www.desmos.com/calculator/uxdnr4k5zl?embed"></graph>
The shaded area to the left of the vertical line x = 3 represents all values of x that make the inequality true.
To graph the solution to the inequality x - 4 ≤ -1, we can start by graphing the line x - 4 = -1.
To graph this line, we can rewrite the equation as x = 3. This tells us that the line is a vertical line passing through the point (3, 0).
Next, we need to determine which side of the line represents the solution to the inequality x - 4 ≤ -1. To do this, we can choose a test point on one side of the line and substitute its coordinates into the inequality.
Let's choose the point (0, 0), which is below the line. Substituting these coordinates into the inequality, we have 0 - 4 ≤ -1, which simplifies to -4 ≤ -1. Since this statement is true, we know that the area below the line represents the solution to the inequality.
Therefore, the graph of the solution to the inequality x - 4 ≤ -1 is the region below the line x = 3.
To find the solution to the inequality, we can first isolate the variable x.
1. Start with the given inequality: x - 4 ≤ -1
2. Add 4 to both sides of the inequality: x - 4 + 4 ≤ -1 + 4
3. Simplify: x ≤ 3
Now that we have the simplified inequality x ≤ 3, we can represent its solution on a number line or graph.
To graph the solution x ≤ 3, it means all the values of x that are less than or equal to 3. On a number line, you can represent this as a closed circle (to include the value 3) at 3, and shade to the left to show all the values less than 3.
So, the graph that shows the solution to the inequality x - 4 ≤ -1 is a number line with a closed circle at 3, and shading to the left.