Final answer:
The inequality is solved by distributing the -3, moving all h terms to one side, and constants to the other, then isolating g by dividing by 30. This results in the inequality g < h/10 + 5/6.
Step-by-step explanation:
To solve the inequality -6h - 3(-10g + 10) < -3h + 5 - 10, first distribute the -3 on the left side of the inequality:
-6h + 30g - 30 < -3h - 5
Now, add 6h to both sides to get all the h terms on one side, and simplify:
30g - 30 < 3h - 5
Then, add 30 to both sides to get all constants on one side:
30g < 3h + 25
Finally, to solve for g, divide both sides by 30:
g < h/10 + 25/30
g < h/10 + 5/6
Remember, when multiplying or dividing an inequality by a negative number, the direction of the inequality sign must be reversed. However, in this case, since we divided by a positive number (30), the inequality sign remains the same.