Final answer:
The equation 2/5(10h+5) = 4h + 2.5 simplifies to 0 = 0.5 after distributing and combining like terms, indicating there is no solution as the statement is untrue.
Step-by-step explanation:
The student's algebraic equation is 2/5(10h+5) = 4h + 2.5. To solve the equation, follow these steps:
- Distribute the 2/5 through the parentheses: 2/5 * 10h + 2/5 * 5.
- Simplify the distributed terms: 4h + 2.
- Bring all terms involving h to one side and constant terms to the other side: 4h - 4h = 2.5 - 2.
- Simplify both sides of the equation: 0h = 0.5.
- Since the term with h is eliminated and we are left with an untrue statement, this indicates there's no solution.
In this particular case, the equation simplifies to a form that implies there are no solutions because the variable h is eliminated, leaving a statement that is not true (0 does not equal 0.5).