The equation for "the distance from x to -4 is less than 12" is
|x-4|<12?
I'm just checking my answers.
nope. That is the distance from x to 4.
Try marking a number line. The distance from x to h is |x - h|.
So then it would be |x+4|
correct.
You are correct! The equation to represent "the distance from x to -4 is less than 12" is indeed |x - (-4)| < 12, which can be further simplified as |x + 4| < 12.
To explain how to arrive at this equation, let's break it down step by step:
1. Start with the phrase "the distance from x to -4." This means we want to find the absolute value of the difference between x and -4.
2. The absolute value of a number is always positive, so we can express this absolute value using the absolute value notation, denoted by | |.
3. The difference between two numbers can be expressed as the subtraction of one number from another. In this case, we want to subtract -4 from x, so we write x - (-4).
4. Finally, we want the result to be less than 12. In mathematical notation, this is represented by the "<" symbol. Therefore, the equation becomes |x - (-4)| < 12.
After simplifying the equation further, we get |x + 4| < 12.