To graph the absolute value equation |2x - 1| = 5 on a number line, follow these steps:
Step 1: Write the equation in two separate equations, one positive and one negative, since the absolute value can be positive or negative:
- 2x - 1 = 5
- -(2x - 1) = 5
Step 2: Solve each equation for x:
- 2x = 6 (add 1 to both sides)
x = 3 (divide both sides by 2)
- -2x + 1 = 5 (distribute the negative sign)
-2x = 4 (subtract 1 from both sides)
x = -2 (divide both sides by -2)
Step 3: Mark the solutions on the number line:
Place a closed circle at x = 3 (since |2x - 1| = 5 when 2x - 1 = 5), and another closed circle at x = -2 (since |2x - 1| = 5 when -(2x - 1) = 5).
Step 4: Draw a line segment connecting the two points:
Draw a line segment between the closed circles representing the solutions.
Step 5: Indicate the regions where the absolute value is positive or negative:
Since the absolute value is equal to 5, there will be two regions on the number line. Mark the region to the left of x = -2 as "Negative" and the region to the right of x = 3 as "Positive."
The graph of the absolute value equation |2x - 1| = 5 on a number line will look like this:
-3 -2 -1 0 1 2 3 4 5
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | |
| | | | |
- |-----------+-----------+-----------+-----------| +
| | | | |
+ |-----------+-----------+-----------+-----------| -
| | | | |
| | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+
Or the Image: