Use the image to answer the question.
A number line with arrows at both the ends ranges from negative 90 to negative 30 in increments of 1, but labeled in increments of 10. A closed circle is placed on negative 33 and on negative 89. A curved arrow is drawn leftward starting from negative 33 to negative 43 and is labeled as negative 10. Four more curved arrows are drawn from negative 43 to negative 53, negative 53 to negative 63, negative 63 to negative 73, and negative 73 to negative 83, all labeled as negative 10. A final curved arrow from negative 83 to negative 89 is labeled as negative 6.
What equation represents the model shown?
The model shows a number line ranging from negative 90 to negative 30, with increments of 1 labeled in increments of 10. The closed circle on negative 33 suggests that negative 33 is included in the solution set. The curved arrow labeled negative 10 indicates that the numbers decrease by 10 as we move leftward.
From negative 33, the arrow reaches negative 43. From negative 43, the arrow reaches negative 53. This pattern continues until the arrow reaches negative 83. From negative 83, the arrow reaches negative 89, with a decrease of 6.
Therefore, the equation that represents this model is: x ≤ -33 and x ≥ -89 with x decreasing by 10, except for the last arrow where x decreases by 6.
The given model shows a number line ranging from negative 90 to negative 30 in increments of 1, but labeled in increments of 10.
A closed circle is placed on negative 33 and another on negative 89.
From negative 33, a curved arrow pointing leftward is drawn up to negative 43, labeled as negative 10.
Then, four more curved arrows are drawn, each labeled as negative 10, going from negative 43 to negative 53, negative 53 to negative 63, negative 63 to negative 73, and negative 73 to negative 83.
Finally, a curved arrow from negative 83 to negative 89 is drawn, labeled as negative 6.
Based on this information, we can determine the equation that represents the model shown.
Starting from negative 33, we have a series of five curved arrows, each labeled as negative 10.
So, the equation that represents this series can be written as:
x = -33 - (10 * n), where n represents the number of curved arrows and x represents the position on the number line.
Substituting the values, we can write the equation for the series of five curved arrows as:
x = -33 - (10 * (n - 1)), where n ranges from 1 to 5.
For the final curved arrow from negative 83 to negative 89, the label is negative 6.
So, we can write the equation for this curved arrow as:
x = -83 + (-6 * (n - 1)), where n ranges from 1 to 1.
Hence, the equation that represents the entire model shown is a combination of the two equations:
For the series: x = -33 - (10 * (n - 1)), where n ranges from 1 to 5, and
For the final curved arrow: x = -83 + (-6 * (n - 1)), where n ranges from 1 to 1.