Question

Solve for hh in the equation 5(3h-9) - 12 = 12 - 7(h-9). provide a step-by-step solution, demonstrating each step of the algebraic process leading to the solution for h."

Answer 1

To solve for h in the equation 5(3h-9) - 12 = 12 - 7(h-9), we expand brackets, simplify both sides, combine like terms, and solve for h which results in h = 6.

Step-by-step explanation:

The correct answer is option C, where we solve for h in the given algebraic equation. To solve the equation 5(3h-9) - 12 = 12 - 7(h-9), we follow the algebraic process:

1. Expand the brackets:
   15h - 45 - 12 = 12 - 7h + 63.
2. Simplify both sides:
   15h - 57 = 75 - 7h.
3. Add 7h to both sides:
   15h + 7h - 57 = 75.
4. Combine like terms:
   22h - 57 = 75.
5. Add 57 to both sides:
   22h = 132.
6. Divide both sides by 22 to solve for h:
   h = 132 / 22.
7. Therefore, h equals 6.

Remember to check the answer to ensure it is reasonable by substituting it back into the original equation.