To solve the absolute value inequality 2x – 4 < 14, we first need to isolate the absolute value expression on one side of the inequality.
Step 1: Add 4 to both sides of the inequality:
2x – 4 + 4 < 14 + 4
2x < 18
Step 2: Next, we divide both sides by 2:
x < 9
Since this is a simple absolute value inequality without a negative case to consider, there is no need to split into cases. The solution to the inequality is:
x < 9
Now, let’s graph this solution. To represent this on a number line:
- Draw a number line.
- Mark the point 9 on the line.
- Since the inequality is strict (<), we will use an open circle at 9 to indicate that 9 is not included in the solution set.
- Shade the portion of the number line to the left of 9 to represent all values less than 9.
This graph visually represents all the values of x that satisfy the inequality 2x – 4 < 14.