Final answer:
To solve the equation −16−10.2g=−14.7g+16.85, combine like terms and isolate the variable g. The solution is g = 7.3. To check the solution, substitute g = 7.3 back into the equation and verify that both sides are equal.
Step-by-step explanation:
To solve the equation −16−10.2g=−14.7g+16.85, we can start by combining like terms. Adding 14.7g to both sides of the equation, we have -16 - 10.2g + 14.7g = 16.85. Simplifying the equation, we get -16 + 4.5g = 16.85. Next, we can isolate the variable by subtracting -16 from both sides: 4.5g = 16.85 + 16 = 32.85. Finally, we can solve for g by dividing both sides of the equation by 4.5 to get g = 7.3.
To check our solution, we can substitute g = 7.3 back into the original equation and see if it holds true. We have: -16 - 10.2(7.3) = -14.7(7.3) + 16.85. Simplifying both sides of the equation, we get -16 - 74.46 = -107.31 + 16.85. This simplifies to -90.46 = -90.46, which is true. Therefore, the solution to the equation is g = 7.3.