Solve and Graph the Absolute Value Inequality 2x – 4 < 8

To solve the absolute value inequality 2x – 4 < 8, we follow these steps:

1. Start by isolating the absolute value expression. We can do this by adding 4 to both sides:

2x - 4 + 4 < 8 + 4
2x < 12

2. Next, divide both sides by 2:

x < 6

3. Now we need to consider the other side of the absolute value inequality, which is when the expression is less than -8. We set it up as follows:

2x - 4 > -8

4. Add 4 to both sides again:

2x - 4 + 4 > -8 + 4
2x > -4

5. And divide by 2:

x > -2

Combining both parts of the solution, we find that:

-2 < x < 6

This gives us the solution where x is between -2 and 6.

To graph the solution:

• Plot open circles at -2 and 6 on a number line to indicate that these points are not included in the solution.
• Shade the region between -2 and 6 to represent all the values of x that satisfy the inequality.

The final solution, -2 < x < 6, indicates all numbers x that lie in this range.