Sure, let's solve the given equation step-by-step:
Given equation:
[tex]\[ 4|0.5x - 2.5| = 0 \][/tex]
### Step 1: Isolate the Absolute Value Expression
To isolate the absolute value expression, we first divide both sides of the equation by 4:
[tex]\[ |0.5x - 2.5| = 0 \][/tex]
### Step 2: Understand the Property of Absolute Value
The absolute value of a number is zero only if the number itself is zero. Therefore, we have:
[tex]\[ 0.5x - 2.5 = 0 \][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
Now, we solve the equation [tex]\( 0.5x - 2.5 = 0 \)[/tex].
First, add 2.5 to both sides of the equation:
[tex]\[ 0.5x = 2.5 \][/tex]
Then, divide both sides by 0.5:
[tex]\[ x = \frac{2.5}{0.5} \][/tex]
[tex]\[ x = 5 \][/tex]
### Conclusion
The solution to the equation [tex]\( 4|0.5x - 2.5| = 0 \)[/tex] is:
[tex]\[ x = 5 \][/tex]
### Answer
[tex]\[ x = 5 \][/tex]
