Solve the compound inequality. Graph the solution.

Question

–2 ≤ 2x – 4 < 4

Answer 1

To solve the compound inequality -2 ≤ 2x - 4 < 4, we need to solve two separate inequalities.

First, let's solve the left inequality -2 ≤ 2x - 4:
-2 + 4 ≤ 2x - 4 + 4
2 ≤ 2x
2/2 ≤ 2x/2
1 ≤ x

Next, let's solve the right inequality 2x - 4 < 4:
2x - 4 + 4 < 4 + 4
2x < 8
2x/2 < 8/2
x < 4

Combining the solutions, we have 1 ≤ x < 4. This means that x must be greater than or equal to 1 but less than 4.

To graph the solution, we will draw a number line and shade the region between 1 and 4, including 1 but not including 4. The shaded region represents the solution to the compound inequality.

Here is the graph of the solution on a number line:
```
---[=======)--------
1 4
```

The shaded region starts at 1 and goes up to, but does not include, 4.