Question

What are the solutions of -1 ≤ x - 3 < 4? Graph the solution.

a) 2 ≤ x < 7
b) -2 ≤ x < 1
c) -4 ≤ x ≤ 1
d) 2 < x ≤ 7

Answer 1

The solution is 2 ≤ x < 7. Option (a) is true.

Explanation:

To find the solutions of the inequality -1 ≤ x - 3 < 4, we can solve it step by step.

First, we'll add 3 to all parts of the inequality:

-1 + 3 ≤ x - 3 + 3 < 4 + 3

2 ≤ x < 7

Now, let's graph the solution on a number line as given below.

The graph shows a filled-in circle at 2 and a hollow circle at 7, indicating that x is greater than or equal to 2 and less than 7.

This aligns with the solution we found, 2 ≤ x < 7.

Thus, option (a) is true.