which inequality matches the graph a. 2n + 5 ≤ 7n b. 2n – 5 < 7 c. 2n + 5 < 7 d .2n + 5 ≥ 7
To determine which inequality matches the given graph, let's analyze each option:
a) 2n + 5 ≤ 7n
This inequality states that "2n + 5" is less than or equal to "7n". Notice that in this case, if you subtract "2n" from both sides of the equation, we get "5" is less than or equal to "5n". Simplifying further, we can divide both sides of the equation by 5, resulting in "1" being less than or equal to "n". This means that for this inequality, the values of "n" would include all numbers greater than or equal to 1.
b) 2n – 5 < 7
This inequality states that "2n – 5" is less than "7". To find the value of "n", we can add "5" to both sides of the equation, giving us "2n" is less than "12". By dividing both sides of the equation by "2", we find that "n" is less than "6". This means that for this inequality, the values of "n" would include all numbers less than 6.
c) 2n + 5 < 7
This inequality states that "2n + 5" is less than "7". We can find the value of "n" by subtracting "5" from both sides of the equation, resulting in "2n" being less than "2". Dividing both sides of the equation by "2", we see that "n" is less than "1". Therefore, for this inequality, the values of "n" would include all numbers less than 1.
d) 2n + 5 ≥ 7
This inequality states that "2n + 5" is greater than or equal to "7". Subtracting "5" from both sides of the equation, we have "2n" is greater than or equal to "2". Dividing both sides of the equation by "2", we find that "n" is greater than or equal to "1". Therefore, for this inequality, the values of "n" would include all numbers greater than or equal to 1.
Based on the analysis above, the inequality that matches the given graph is option d) 2n + 5 ≥ 7.
To determine which inequality matches the given graph, we need to analyze the equation that represents the graph.
Looking at the options:
a. 2n + 5 ≤ 7n
b. 2n – 5 < 7
c. 2n + 5 < 7
d. 2n + 5 ≥ 7
Let's analyze each option and see which one matches the graph.
Option a. 2n + 5 ≤ 7n:
This inequality indicates that the left side is less than or equal to the right side. However, the graph does not show a solid line (≤) but rather a dashed line (<), so option a is not a match.
Option b. 2n – 5 < 7:
This inequality suggests that the left side is less than the right side. Looking at the graph, it shows a dashed line (<) which represents that the left side is strictly less than the right side. Therefore, option b matches the graph.
Option c. 2n + 5 < 7:
This inequality implies that the left side is less than the right side. The graph also shows a dashed line (<), indicating that the left side is strictly less than the right side. Hence, option c matches the graph.
Option d. 2n + 5 ≥ 7:
This inequality states that the left side is greater than or equal to the right side. However, the graph does not show a solid line (≥) but rather a dashed line (<), so option d is not a match.
In conclusion, the inequalities that match the given graph are options b. 2n – 5 < 7 and c. 2n + 5 < 7.