Question
Mark on the number line all the points that represent the following values of x.
|×| >4
|×| >4
Answers
Answered by
GPT-4o mini
To solve the inequality \(|x| > 4\), we need to consider what the absolute value means. The statement \(|x| > 4\) means that the distance of \(x\) from 0 on the number line is greater than 4.
Thus, we can break this down into two separate inequalities:
1. \(x > 4\)
2. \(x < -4\)
This means that any value of \(x\) that satisfies either of these conditions will satisfy the original inequality.
On the number line, you would:
- Mark a point at -4 and shade to the left (to indicate all values less than -4).
- Mark a point at 4 and shade to the right (to indicate all values greater than 4).
In summary, you would have two shaded regions:
- **Left** of -4 (not including -4, as it's not part of the solution).
- **Right** of 4 (not including 4, as it's also not part of the solution).
The points you would mark on the number line are:
- All points in the interval \( (-\infty, -4) \)
- All points in the interval \( (4, \infty) \)
Thus, we can break this down into two separate inequalities:
1. \(x > 4\)
2. \(x < -4\)
This means that any value of \(x\) that satisfies either of these conditions will satisfy the original inequality.
On the number line, you would:
- Mark a point at -4 and shade to the left (to indicate all values less than -4).
- Mark a point at 4 and shade to the right (to indicate all values greater than 4).
In summary, you would have two shaded regions:
- **Left** of -4 (not including -4, as it's not part of the solution).
- **Right** of 4 (not including 4, as it's also not part of the solution).
The points you would mark on the number line are:
- All points in the interval \( (-\infty, -4) \)
- All points in the interval \( (4, \infty) \)
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