Kateandsophidn
Answered

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What is the solution to [tex]$4|0.5 x - 2.5| = 0$[/tex]?

A. [tex]x = 1.25[/tex]
B. [tex]x = 5[/tex]
C. [tex]x = -1.25 \text{ or } x = 1.25[/tex]
D. [tex]x = -5 \text{ or } x = 5[/tex]

Sagot :

GinnyAnsweridn
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]
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