Question

Solve for [h]. Give an exact answer. [3h = 7(2/7 - 3/7h) - 10]

Answer 1

To solve for [h] in the equation 3h = 7(2/7 - 3/7h) - 10, distribute the 7 to both terms inside the parentheses, simplify the fractions, combine like terms, and multiply both sides by the reciprocal to isolate [h]. The solution is h = -63/168.

Step-by-step explanation:

To solve for [h] in the equation 3h = 7(2/7 - 3/7h) - 10, we can follow these steps:

1. Distribute the 7 to both terms inside the parentheses:
2. 3h = 7(2/7) - 7(3/7h) - 10
3. Simplify the fractions:
4. 3h = 1 - 3/7h - 10
5. Combine like terms:
6. 3h + 3/7h = 1 - 10
7. 24/7h = -9
8. Multiply both sides by 7/24 to isolate [h]:
9. 7/24 * 24/7h = -9 * 7/24
10. h = -rac{9}{24} * rac{7}{7}
11. [h] = -rac{63}{168}