Which statement is true?
$-1.2>6.9$
$6.9<1.2$
$-6.9<-1.2$
$1.2<-6.9$
Answer (2)
Compare the numbers in each inequality.
6.9"> − 1.2 > 6.9 is false.
6.9 < 1.2 is false.
− 6.9 < − 1.2 is true.
1.2 < − 6.9 is false.
The true statement is − 6.9 < − 1.2 .
Explanation
Analyzing the Inequalities We are given four inequalities and need to identify the true one. Let's analyze each:
6.9"> − 1.2 > 6.9 : A negative number cannot be greater than a positive number. This statement is false.
6.9 < 1.2 : 6.9 is greater than 1.2. This statement is false.
− 6.9 < − 1.2 : On the number line, -6.9 is to the left of -1.2, meaning -6.9 is less than -1.2. This statement is true.
1.2 < − 6.9 : A positive number cannot be less than a negative number. This statement is false.
Identifying the True Statement Therefore, the only true statement is − 6.9 < − 1.2 .
Examples
Understanding inequalities is crucial in many real-life situations. For instance, when managing personal finances, you might compare your debt (negative numbers) to your savings (positive numbers). Knowing that -$100 is less than -$50 helps you understand that owing $100 is worse than owing $50. Similarly, in science, comparing temperatures below zero helps us understand relative coldness, where -10°C is colder than -5°C. These comparisons are fundamental in making informed decisions.
The true statement among the four given inequalities is − 6.9 < − 1.2 . All other statements are false as they do not hold mathematically. This understanding of inequalities is important for making comparisons between numbers.
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