Question

what is the solution to $4|0.5x - 2.5| = 0?$○ $x = 1.25$○ $x = 5$○ $x = -1.25$ or $x = 1.25$○ $x = -5$ or $x = 5$

Explanation:

Step1: Isolate the absolute value

Divide both sides by 4:
$\frac{4|0.5x - 2.5|}{4} = \frac{0}{4}$
Simplify to get:
$|0.5x - 2.5| = 0$

Step2: Solve the linear equation

An absolute value equals 0 only when the expression inside is 0:
$0.5x - 2.5 = 0$

Step3: Solve for x

Add 2.5 to both sides:
$0.5x = 2.5$
Divide both sides by 0.5:
$x = \frac{2.5}{0.5} = 5$

Answer:

x = 5