Solve the compound inequality. Graph the solution.

Question

–2 ≤ 2x – 4 < 4

Answer 1

To solve the compound inequality -2 ≤ 2x - 4 < 4, we can solve it as two separate inequalities:

First inequality: -2 ≤ 2x - 4
Adding 4 to both sides of the inequality, we get:
2 ≤ 2x
Dividing both sides by 2 (which is positive), we get:
1 ≤ x

Second inequality: 2x - 4 < 4
Adding 4 to both sides of the inequality, we get:
2x < 8
Dividing both sides by 2 (which is positive), we get:
x < 4

So the solution to the compound inequality is 1 ≤ x < 4.

Now let's graph the solution on the number line:

First, mark all the points from 1 to 4 on the number line, including 1 but not 4.
<---|-----|-----|-----|-----|-----|----->
-1 0 1 2 3 4 5

Since x is greater than or equal to 1, we place a closed circle at 1, indicating that it is included in the solution.
<---|-----|-----|-----|-----|-----|----->
-1 0 [1] 2 3 4 5

Since x is less than 4, we place an open circle at 4, indicating that it is not included in the solution.
<---|-----|-----|-----|-----|-----|----->
-1 0 [1] 2 3 ]4[ 5

Finally, we shade the region between 1 and 4.
<---|=====|=====|-----|-----|-----|----->
-1 0 [1] 2 3 ]4[ 5

This shaded region represents the solution to the compound inequality -2 ≤ 2x - 4 < 4.