Which inequality is true when the value of $c$ is $19$?
-c-9 \geq 4
-c-9 \geq-4
-c-9 \leq 4
c-9 \leq-4
Answer (2)
Substitute c = 19 into each inequality.
Evaluate each inequality to determine if it is true or false.
− 19 − 9 ≥ 4 is false, − 19 − 9 ≥ − 4 is false, − 19 − 9 ≤ 4 is true, and 19 − 9 ≤ − 4 is false.
The inequality that is true when c = 19 is − c − 9 ≤ 4 .
Explanation
Problem Analysis We are given the value of c as 19 and four inequalities:
− c − 9 ≥ 4
− c − 9 ≥ − 4
− c − 9 ≤ 4
c − 9 ≤ − 4
Our goal is to determine which of these inequalities is true when c = 19 .
Substituting and Evaluating Let's substitute c = 19 into each inequality and evaluate:
− 19 − 9 ≥ 4 ⇒ − 28 ≥ 4 . This is false.
− 19 − 9 ≥ − 4 ⇒ − 28 ≥ − 4 . This is false.
− 19 − 9 ≤ 4 ⇒ − 28 ≤ 4 . This is true.
19 − 9 ≤ − 4 ⇒ 10 ≤ − 4 . This is false.
Identifying the True Inequality After substituting c = 19 into the inequalities and evaluating them, we find that only the third inequality, − c − 9 ≤ 4 , is true.
Final Answer Therefore, the inequality that is true when c = 19 is − c − 9 ≤ 4 .
Examples
Understanding inequalities is crucial in many real-world scenarios. For instance, when budgeting, you might use inequalities to determine how much you can spend on different items while staying within your financial limits. Similarly, in science, inequalities can help define the range of acceptable values for experimental parameters. In everyday life, inequalities are used to compare prices, distances, and quantities to make informed decisions.
The inequality that is true when c = 19 is − c − 9 ≤ 4 . After substituting c and evaluating all options, only this inequality holds true. The others were found to be false.
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