Step-by-step explanation And Answer:
To solve the inequality |x + 9| < 0.001 and express the answer using interval notation, let's break it down into two cases:
Case 1: x + 9 > 0
In this case, the absolute value of x + 9 is equal to (x + 9). So we have:
x + 9 < 0.001
Subtracting 9 from both sides gives us:
x < -8.999
Case 2: x + 9 < 0
In this case, the absolute value of x + 9 is equal to -(x + 9). So we have:
-(x + 9) < 0.001
Multiplying both sides by -1 reverses the inequality sign:
x + 9 > -0.001
Subtracting 9 from both sides gives us:
x > -9.001
Combining the solutions from both cases, we have:
x < -8.999 or x > -9.001
Expressing this using interval notation, we can write the solution as:
(-∞, -8.999) U (-9.001, ∞)
This means that x can take any value less than -8.999 or any value greater than -9.001, but it cannot equal -8.999 or -9.001.