Match the inequality to the graph of its solution.
n/4≤-1
-10x≥-100
5x≥20
n/4 ≤ -1: Graph C
-10x ≥ -100: Graph A
5x ≥ 20: Graph B
To match the inequality to the graph of its solution, we can solve each inequality and then analyze the graph.
1) n/4 ≤ -1:
To solve this inequality, we can multiply both sides by 4 to get rid of the fraction:
n ≤ -4
This inequality represents all numbers less than or equal to -4 on the number line. The graph of this solution would be a line with a closed circle at -4, extending to the left.
2) -10x ≥ -100:
We can solve this inequality by dividing both sides by -10. However, we need to flip the direction of the inequality because we are dividing by a negative number:
x ≤ -100/-10
x ≤ 10
This inequality represents all numbers less than or equal to 10 on the number line. The graph would be a line with a closed circle at 10, extending to the left.
3) 5x ≥ 20:
To solve this inequality, we can divide both sides by 5:
x ≥ 20/5
x ≥ 4
This inequality represents all numbers greater than or equal to 4 on the number line. The graph would be a line with a closed circle at 4, extending to the right.
So, to match the inequalities to their respective graphs:
1) n/4 ≤ -1 -----------Graph: A line to the left with a closed circle at -4.
2) -10x ≥ -100 ------Graph: A line to the left with a closed circle at 10.
3) 5x ≥ 20 ------------Graph: A line to the right with a closed circle at 4.
To match the inequality to the graph of its solution, we first need to solve each inequality.
Let's start with the first inequality:
n/4 ≤ -1
To solve this inequality, we can multiply both sides of the inequality by 4 to isolate n:
n ≤ -4
Now, let's move on to the second inequality:
-10x ≥ -100
To solve this inequality, we can divide both sides of the inequality by -10. However, since we are dividing by a negative number, we need to reverse the inequality sign:
x ≤ 10
Finally, we have the third inequality:
5x ≥ 20
To solve this inequality, we can divide both sides of the inequality by 5:
x ≥ 4
Now, let's match each inequality to its corresponding graph:
1. n/4 ≤ -1: This inequality represents all values of n that are less than or equal to -4. The graph would be a line with a closed circle at -4, extending infinitely to the left.
2. -10x ≥ -100: This inequality represents all values of x that are greater than or equal to 10. The graph would be a line with a closed circle at 10, extending infinitely to the right.
3. 5x ≥ 20: This inequality represents all values of x that are greater than or equal to 4. The graph would be a line with a closed circle at 4, extending infinitely to the right.
Note: The inequalities involving "less than or equal to" and "greater than or equal to" use closed circles to represent the endpoints, indicating that those values are included in the solution set.