Match the inequality to the graph of its solution.(2 points)
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n over 4≤ –1
–10x ≥ –100
5x ≥ 20
A number line is labeled from negative 10 to 10. There is a closed circle on 10 and the line is shaded to the left.A number line is labeled from negative 10 to 10. There is a closed circle on negative 4 and the line is shaded to the left.A number line is labeled from negative 10 to 10. There is a closed circle on 4 and the line is shaded to the right.
The inequality "-10x ≥ –100" matches the graph with a closed circle on 10 and the line shaded to the left.
The inequality "n over 4≤ –1" matches the graph with a closed circle on negative 4 and the line shaded to the left.
The inequality "5x ≥ 20" matches the graph with a closed circle on 4 and the line shaded to the right.
n over 4 ≤ –1 -> A number line is labeled from negative 10 to 10. There is a closed circle on negative 4 and the line is shaded to the left.
-10x ≥ –100 -> A number line is labeled from negative 10 to 10. There is a closed circle on 10 and the line is shaded to the left.
5x ≥ 20 -> A number line is labeled from negative 10 to 10. There is a closed circle on 4 and the line is shaded to the right.
To match the inequalities to their corresponding graphs, we need to analyze each inequality statement.
1) n/4 ≤ -1
This inequality can be solved by multiplying both sides of the inequality by 4 to remove the fraction. When we multiply by a negative number (in this case, 4), we need to reverse the inequality sign.
So, n ≤ -4.
The solution to this inequality is all numbers less than or equal to -4.
2) -10x ≥ -100
To solve this inequality, we need to divide both sides by -10. When dividing by a negative number, we also need to reverse the inequality sign.
So, x ≤ 10.
The solution to this inequality is all numbers less than or equal to 10.
3) 5x ≥ 20
To solve this inequality, we need to divide both sides by 5. There is no need to reverse the inequality sign since we are dividing by a positive number.
So, x ≥ 4.
The solution to this inequality is all numbers greater than or equal to 4.
Based on the explanations above, let's match the inequalities to the corresponding graphs:
- n/4 ≤ -1 corresponds to "A number line is labeled from negative 10 to 10. There is a closed circle on 10 and the line is shaded to the left."
- -10x ≥ -100 corresponds to "A number line is labeled from negative 10 to 10. There is a closed circle on negative 4 and the line is shaded to the left."
- 5x ≥ 20 corresponds to "A number line is labeled from negative 10 to 10. There is a closed circle on 4 and the line is shaded to the right."