Final answer:
There are 7 numbers that are 3 units away from 0.
Explanation:
To find the numbers that are 3 units away from 0, we can use the concept of absolute value. Absolute value is the distance of a number from 0 on the number line. In this case, we are looking for numbers that are 3 units away from 0, which means the distance between these numbers and 0 is 3 units.
To visualize this, we can draw a number line and mark 0 as the midpoint. Then, we can count 3 units to the left and right of 0. This would give us the numbers -3 and 3. However, since the question asks for numbers that are 3 units away from 0, we also need to consider the numbers on either side of -3 and 3, which are -4 and 4 respectively. Therefore, the numbers that are 3 units away from 0 are -4, -3, 0, 3, and 4.
Another way to approach this problem is by using algebraic expressions. Let's represent the numbers that are 3 units away from 0 as x. We can then write the equation |x| = 3, where |x| represents the absolute value of x. To solve this equation, we need to consider two cases: when x is positive and when x is negative.
Case 1: When x is positive, the equation |x| = 3 becomes x = 3. Therefore, the positive number that is 3 units away from 0 is 3.
Case 2: When x is negative, the equation |x| = 3 becomes -x = 3. Solving for x, we get x = -3. However, we also need to consider the numbers on either side of -3, which are -4 and -2.
Hence, the numbers that are 3 units away from 0 are -4, -3, -2, 0, 2, 3, and 4. In conclusion, there are 7 numbers that are 3 units away from 0.