Question

Determine the location of a point \((x, y, z)\) that satisfies the condition(s). \(|x|>4\)

Short answer

The location of the points that satisfy the condition \(|x|>4\) are all points in the 3D space where x is less than -4 or more than 4, with no conditions on y and z, i.e., they can be any real number.

Step-by-step solution

Understand the absolute value inequality

The absolute value \(|x|\) means the distance of x from the origin on the number line. That distance is always positive (or zero). The inequality \(|x|>4\) signifies that the distance of x from the origin is more than 4. This means x is either more than 4 units to the right of the origin or more than 4 units to the left of the origin.

Figure out the values of x

Given inequality is \(|x|>4\), which boasts solutions where x is less than -4 and greater than 4. Hence, the solutions are x<-4 and x>4.

Determine the location in 3D space

Since there're no conditions given for y and z, the values for y and z could be any real numbers. Therefore, the points that satisfy the conditions are located everywhere in the 3D space for \(x<-4\) and \(x>4\), with y and z being any real numbers