Answer :
Let's solve the equation [tex]\(4x - 32 = 0\)[/tex] step-by-step.
### Step-by-Step Solution
1. Write down the equation:
[tex]\[ 4x - 32 = 0 \][/tex]
2. Add 32 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ 4x = 32 \][/tex]
3. Divide both sides by 4 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{32}{4} \][/tex]
[tex]\[ x = 8 \][/tex]
So, the solution is [tex]\( x = 8 \)[/tex].
### Graphing the Solution on the Number Line
To graph [tex]\( x = 8 \)[/tex] 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 [tex]\(4x - 32 = 0\)[/tex].
### Step-by-Step Solution
1. Write down the equation:
[tex]\[ 4x - 32 = 0 \][/tex]
2. Add 32 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ 4x = 32 \][/tex]
3. Divide both sides by 4 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{32}{4} \][/tex]
[tex]\[ x = 8 \][/tex]
So, the solution is [tex]\( x = 8 \)[/tex].
### Graphing the Solution on the Number Line
To graph [tex]\( x = 8 \)[/tex] 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 [tex]\(4x - 32 = 0\)[/tex].
