Final answer:
The value that makes the equation 10/x = 1/2x + 38 true is x = 0.25, obtained by cross-multiplying and simplifying the equation.
Step-by-step explanation:
To find the value(s) that satisfy the equation 10/x = 1/2x + 38, we first multiply both sides by 2x to eliminate the fractions:
- 2x * (10/x) = 2x * (1/2x + 38)
- 20 = 1 + 76x
- 19 = 76x
- x = 19/76 = 0.25
The value that makes the equation true is x = 0.25.