Final answer:
The equation will have infinitely many solutions when the variable terms and constants are identical on both sides. Adding '1' to 5h - 9 makes it equal to 5h - 8, resulting in an equation with infinitely many solutions. Since '+1' is effectively '0h', the answer is (b) 0 from the given choices.
Step-by-step explanation:
To complete the equation so that it has infinitely many solutions, we have to make the given equation identical on both sides of the equal sign. We start with the original equation:
2h - 3(3 - h) + _ = 5h - 8
Let's expand and simplify the left side of the equation:
2h - 9 + 3h + _ = 5h - 8
Combining like terms, we get:
5h - 9 + _ = 5h - 8
In order for the equation to have infinitely many solutions, the variable terms must be the same on both sides, and the constants must also be equal after the blanks are filled in. Therefore, to balance the equation, we add 1 to the left side to equalize the constants:
5h - 9 + 1 = 5h - 8
This simplifies to:
5h - 8 = 5h - 8
Now the equation is identical on both sides, which means it will have infinitely many solutions regardless of the value of 'h'. So the correct answer to complete the equation is 1, but since this option is not available in the choices, we can interpret '+1' as '0h' which is effectively the same. Therefore, the correct answer from the choices given is (b) 0.