Final answer:
To solve the equation 5 + 9q = 8 + 8gq, we can isolate the terms with q on one side of the equation and solve for q. Checking the solution involves substituting the value of q back into the original equation. An example calculation is provided to illustrate the process.
Step-by-step explanation:
Solving the Equation:
- Start by subtracting 8 from both sides of the equation to isolate the terms with q on one side.
- Combine like terms on each side of the equation.
- Next, divide both sides of the equation by (9-8g) to solve for q.
- Simplify the equation if possible.
- The solution for q is calculated.
Checking the Solution:
To check if the solution is correct, substitute the value of q found back into the original equation. If the equation is balanced, then the solution is correct.
Example:
If g = 2, substitute g into the original equation: 5 + 9q = 8 + 8(2).
Simplify the equation: 5 + 9q = 8 + 16.
Combine like terms: 9q + 5 = 24.
Subtract 5 from both sides: 9q = 19.
Divide both sides by (9-8g): q = 19/(9-8(2)).
Calculate the solution: q = 19/(-7) = -2.71.
Substituting q = -2.71 back into the original equation: 5 + 9(-2.71) = 8 + 8(2).
Simplify the equation: 5 - 24.39 = 8 + 16.
Combine like terms: -19.39 = 24.
The equation is not balanced, so the solution is incorrect.