Write an absolute value inequality to fit the graph below:
There is a Number line with 14 on the left and 26 on the right with solid dots on both.
Midway between 14 and 26 is 20.
|x-20| <= 6
To write an absolute value inequality to fit the given graph, we need to consider the solid dots on both ends of the number line.
Since there are solid dots on both 14 and 26, it suggests that the numbers 14 and 26 themselves are included in the solution.
Therefore, the absolute value inequality can be written as:
| x - 20 | ≤ 6
This inequality states that the distance between x and 20 is less than or equal to 6 units.
To write an absolute value inequality based on the given graph, we need to determine the values that fall within the range of the solid dots.
The graph indicates that both 14 and 26 are included, so we can start by writing an inequality that includes these values. The absolute value of a number refers to the distance of that number from zero on a number line. Therefore, an absolute value inequality will include two parts: one for the positive distance and one for the negative distance.
In this case, the solid dots represent the numbers 14 and 26, which are equidistant from zero. So, we can set up the inequality as follows:
| x - 20 | ≤ d
The number 20 represents the midpoint between 14 and 26, which is ((14 + 26) / 2 = 20). The variable x represents any number that falls within the given range, and d represents the distance from x to 20.
However, since we want to include the endpoints in the inequality, we need to modify it slightly.
Based on the graph, we can observe that the distance from 20 to either 14 or 26 is 6 units. Therefore, our modified absolute value inequality becomes:
| x - 20 | ≤ 6
This inequality states that the distance between x and 20 is less than or equal to 6 units. It represents all the numbers on the number line that fall within the range defined by the solid dots at 14 and 26.