Question

Solve: `-7\le2x+1<11`



Which number line is the correct representation of the solution?

Answer 1

To solve the compound inequality `-7\le2x+1<11`, we need to isolate the variable `x` in the middle of the inequality.

1) Start by subtracting 1 from all parts of the inequality: -7 - 1 ≤ 2x + 1 - 1 < 11 - 1
This simplifies to: -8 ≤ 2x < 10

2) Divide all parts of the inequality by 2 to solve for `x`: -4 ≤ x < 5

This means that `x` must be greater than or equal to -4 and less than 5.

Using this information, we can represent the solution on a number line:

```
<-------------------------o----x----------------------------------->
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

```

The number line segments from -8 (including -8 itself) up to just before -4 are shaded, indicating that `x` can take any value between -8 and -4 (inclusive). However, any values from -4 up to 5 (not including 5 itself) are left open, indicating that `x` cannot equal 5 but can be any value less than 5. This represents the solution to the given inequality.