Question

Solve and write interval nota |1-x|>=-1

Answer 1

SteTo solve the inequality |1-x|>=-1, we need to consider two cases:

Case 1: x >= 1

In this case, |1-x| simply becomes 1-x. So the inequality becomes:

1-x >= -1

-x >= -2

Multiplying both sides by -1 (and flipping the inequality sign):

x <= 2

The solution for this case is x belongs to (-∞, 2].

Case 2: x < 1

In this case, |1-x| becomes -(1-x) because the expression inside the absolute value will be negative. So the inequality becomes:

-(1-x) >= -1

1-x >= -1

-x >= -2

Multiplying both sides by -1 (and flipping the inequality sign):

x <= 2

But in this case, x < 1, so the solution includes values less than 1. Therefore, the solution for this case is x belongs to (-∞, 2].

Combining the solutions from both cases, we get the final solution:

x belongs to (-∞, 2]p-by-step explanation: