What inequality is correct?
$-9 \geq -9$
$13 \leq 8$
$-5>4$
$123>212$
Answer (1)
Check if − 9 ≥ − 9 is true: − 9 is equal to − 9 , so the inequality is true.
Check if 13 ≤ 8 is true: 13 is greater than 8 , so the inequality is false.
Check if 4"> − 5 > 4 is true: − 5 is less than 4 , so the inequality is false.
Check if 212"> 123 > 212 is true: 123 is less than 212 , so the inequality is false. Therefore, the correct inequality is − 9 ≥ − 9 .
Explanation
Analyzing the Inequalities We are given four inequalities and we need to determine which one is correct. Let's analyze each one.
Evaluating the First Inequality The first inequality is − 9 g e q − 9 . This statement means '-9 is greater than or equal to -9'. Since -9 is equal to -9, the inequality is true.
Evaluating the Second Inequality The second inequality is 13 ≤ 8 . This statement means '13 is less than or equal to 8'. Since 13 is greater than 8, the inequality is false.
Evaluating the Third Inequality The third inequality is 4"> − 5 > 4 . This statement means '-5 is greater than 4'. Since -5 is less than 4, the inequality is false.
Evaluating the Fourth Inequality The fourth inequality is 212"> 123 > 212 . This statement means '123 is greater than 212'. Since 123 is less than 212, the inequality is false.
Conclusion Therefore, the only correct inequality is − 9 g e q − 9 .
Examples
Understanding inequalities is crucial in many real-life situations. For example, when comparing prices, you might use inequalities to determine which product is cheaper. If product A costs $5 and product B costs $7, you can write this as $5 < $7, meaning product A is cheaper. Similarly, inequalities are used in setting speed limits on roads (e.g., speed <= 65 mph) or in financial planning to ensure expenses are less than or equal to income.
