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Two different points on a number line ar...

Two different points on a number line are both 3 units from the point with coordinate −4. The solution to which of the following equations gives the coordinates of both points?

A

|x+4|=3

B

|x-4|=3

C

|x+3|=4

D

|x-3|=4

Text Solution

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The correct Answer is:
To find the coordinates of the two different points that are both 3 units from the point with coordinate -4, we can set up the problem as follows: 1. **Identify the point of reference**: The point on the number line we are considering is -4. 2. **Determine the distance from the reference point**: We are told that the two points are both 3 units away from -4. This means we need to consider both directions on the number line (to the left and to the right). 3. **Set up the equations**: - To find the point that is 3 units to the right of -4, we can write the equation: \[ x = -4 + 3 \] - To find the point that is 3 units to the left of -4, we can write the equation: \[ x = -4 - 3 \] 4. **Combine the equations**: We can express this situation with a single equation that captures both points. We want to find \( x \) such that: \[ |x + 4| = 3 \] This equation states that the distance between \( x \) and -4 is 3 units. 5. **Solve the equation**: The absolute value equation \( |x + 4| = 3 \) can be split into two separate equations: - \( x + 4 = 3 \) - \( x + 4 = -3 \) 6. **Find the solutions**: - For the first equation: \[ x + 4 = 3 \implies x = 3 - 4 \implies x = -1 \] - For the second equation: \[ x + 4 = -3 \implies x = -3 - 4 \implies x = -7 \] Thus, the two points that are 3 units away from -4 are -1 and -7. ### Final Answer: The coordinates of both points are \( -1 \) and \( -7 \).
To find the coordinates of the two different points that are both 3 units from the point with coordinate -4, we can set up the problem as follows: 1. **Identify the point of reference**: The point on the number line we are considering is -4. 2. **Determine the distance from the reference point**: We are told that the two points are both 3 units away from -4. This means we need to consider both directions on the number line (to the left and to the right). 3. **Set up the equations**: - To find the point that is 3 units to the right of -4, we can write the equation: ...
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