Which of the following are true?
A. [tex]$6.8>5.9$[/tex]
B. [tex]$-2.5>-1.9$[/tex]
C. [tex]$-4.7<2.3$[/tex]
D. [tex]$3.5<-7.1$[/tex]
A and B
C and D
A and C
B and D
Answer (2)
Evaluate each inequality: A is true, B is false, C is true, D is false.
Identify the true inequalities: A and C.
Select the correct option: A and C.
The correct answer is A and C: A an d C
Explanation
Analyze the problem We are given four inequalities and asked to determine which ones are true. Then, we must select the answer choice that contains only true statements. Let's evaluate each inequality individually.
Evaluate inequality A A. 5.9"> 6.8 > 5.9 is true because 6.8 is indeed greater than 5.9.
Evaluate inequality B B. -1.9"> − 2.5 > − 1.9 is false because -2.5 is less than -1.9. On the number line, -2.5 is to the left of -1.9.
Evaluate inequality C C. − 4.7 < 2.3 is true because -4.7 is less than 2.3. Negative numbers are always less than positive numbers.
Evaluate inequality D D. 3.5 < − 7.1 is false because 3.5 is greater than -7.1. Positive numbers are always greater than negative numbers.
Determine the correct option Based on our evaluation, inequalities A and C are true, while B and D are false. Therefore, the correct option is A and C.
Examples
Understanding inequalities is crucial in many real-life situations. For example, when comparing prices, you use inequalities to determine which option is cheaper. If one item costs $6.8 and another costs $5.9, the inequality 5.9"> 6.8 > 5.9 tells you that the first item is more expensive. Similarly, in finance, you might use inequalities to compare interest rates or investment returns to make informed decisions.
Upon evaluating the inequalities, we find that A: 5.9"> 6.8 > 5.9 and C: − 4.7 < 2.3 are true, while B and D are false. Therefore, the correct option is A and C.
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