Is the statement true? Explain. $32+(-17)$ is 17 units from 32, in the positive direction.
Answer (2)
Calculate 32 + ( − 17 ) , which equals 15.
Determine the distance between 15 and 32, which is 17.
Check if 15 is in the positive direction from 32. Since 15 < 32, it is in the negative direction.
Conclude that the statement is false because the direction is negative. F a l se
Explanation
Analyzing the Statement Let's analyze the statement: ' 32 + ( − 17 ) is 17 units from 32, in the positive direction'. To determine if this statement is true, we need to calculate 32 + ( − 17 ) , find the distance between the result and 32, and check if the direction is positive.
Calculating the Expression First, we calculate the value of the expression 32 + ( − 17 ) . The result is 15.
Finding the Distance Next, we find the distance between 15 and 32. The distance is ∣15 − 32∣ = ∣ − 17∣ = 17 .
Checking the Direction Now, we need to check if the direction is positive. Since 15 is less than 32, the direction from 32 to 15 is negative, not positive.
Conclusion Since the direction is not positive, the statement is false.
Examples
Understanding number lines and distances is crucial in various real-life scenarios. For instance, consider temperature changes: if the temperature starts at 32 degrees and drops by 17 degrees, the final temperature is 15 degrees. The change is 17 degrees, but it's a decrease, not an increase. Similarly, in financial contexts, if you have $32 and spend $17, you're left with $15, a decrease of $17.
The statement ' 32 + ( − 17 ) is 17 units from 32, in the positive direction' is false. The result of the expression is 15, which is 17 units from 32 in the negative direction. Therefore, the claim about the direction is incorrect.
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