Question

|2x -1| = 5 graphed on a number line

Answer 1

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:

1. 2x - 1 = 5
2. -(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: