Use absolute value notation. The distance between x and -10 is at least 6.
|x-(-10)|>or=6
Is that notation correct?
better is |x-(-10)| >= 6
or |x+10| >= 6
Well, it's kind of correct, but we can spiff it up a bit. Instead of using "x-(-10)" inside the absolute value notation, we can simplify it to "x+10". So, the correct notation would be:
| x + 10 | ≥ 6
Now, doesn't that look much tidier?
No, the absolute value notation for the statement "The distance between x and -10 is at least 6" is incorrect. The correct absolute value notation for this statement would be:
| x - (-10) | ≥ 6
Yes, the notation |x - (-10)| ≥ 6 is correct for expressing that the distance between x and -10 is at least 6 using absolute value notation.
To better understand how this notation is derived, let's break it down step by step:
1. Start with the expression |x - (-10)|: This is the absolute value of the difference between x and -10.
2. The absolute value of a number is always non-negative, so |x - (-10)| is always greater than or equal to 0.
3. The inequality symbol ≥ is used to show that the absolute value expression is greater than or equal to the right-hand side of the inequality.
4. Finally, we have 6 on the right-hand side of the inequality. This means that the absolute value of x - (-10) is greater than or equal to 6, which is exactly what we want to express.
Therefore, the notation |x - (-10)| ≥ 6 correctly represents the statement that the distance between x and -10 is at least 6.