Let's solve the equation \(\(4x - 32 = 0\)\) step-by-step.
### Step-by-Step Solution
1. Write down the equation:
\(\[ 4x - 32 = 0 \]\)
2. Add 32 to both sides to isolate the term with \(\(x\)\):
\(\[ 4x = 32 \]\)
3. Divide both sides by 4 to solve for \(\(x\)\):
\(\[ x = \frac{32}{4} \]\)
\(\[ x = 8 \]\)
So, the solution is \(\( x = 8 \)\).
### Graphing the Solution on the Number Line
To graph \(\( x = 8 \)\) on a number line:
1. Draw a horizontal line and mark even intervals for the numbers.
2. Locate the position of 8 on this number line.
3. Place a solid dot or circle at 8 to represent the solution.
Here's a simple representation of the number line with the solution:
``
<---|---|---|---|---|---|---|---|---|---|--->
2 4 6 8 10
•
(Solution: x = 8)
The solid dot at 8 indicates that this is the solution to the equation \(\(4x - 32 = 0\)\).
