Final answer:
To solve the student's algebraic equation for x, combine like terms, and then isolate the variable x on one side of the equation.
Step-by-step explanation:
The student's equation needs to be solved for x. To do this, we should first combine like terms and then get all the x terms on one side of the equation and the constants on the other side.
The equation provided by the student is:
\(\frac{{2x - 1}}{4} - \frac{{3x - 2}}{5} = \frac{1}{10}\)
To solve the equation, we can follow these steps:
- Multiply both sides of the equation by 20 (the least common multiple of 4, 5, and 10) to eliminate fractions.
- Combine like terms and move all x terms to one side and constants to the other.
- Divide by the coefficient of x to find the value of x.
By following these steps, the student will solve for x.