What linear inequality is shown graphed on the number line? Make sure to write your inequality so that x comes first. And could you explain how you got the answer? :)
A number line reaching from -10 to 10. There is an open circle on 0.25 moving towards the negitive direction.
The linear inequality shown graphed on the number line is:
x < 0.25
To understand how we arrived at this conclusion, let's break down the information provided:
1. The open circle on 0.25: This indicates that 0.25 is not included in the solution set and should be represented with an open circle on the number line.
2. Moving towards the negative direction: This means that the solution set includes all values to the left of 0.25. In other words, x should be less than 0.25.
Combining these two pieces of information, we can write the linear inequality as x < 0.25.
How do you know to write > and < and not ≥ or ≤?
In this specific case, the linear inequality x < 0.25 is indicated by the open circle on 0.25 and movement towards the negative direction.
Using the symbols > (greater than) or < (less than) in an inequality depends on whether the endpoint is included or excluded from the solution set.
An open circle on a specific value, as seen in the given graph, represents that the value is excluded from the solution set. Inequality symbols (>, <) are used to indicate this exclusion.
If the circle were filled or shaded, it would represent that the value is included, and in this case, we would use the symbols ≥ (greater than or equal to) or ≤ (less than or equal to) to indicate the inclusion of the endpoint.
Since the open circle on 0.25 suggests that the value is excluded, we use the inequality symbol < to represent numbers that are strictly less than 0.25.