Solve for j. 8(3j + 8) + 7 = -10 + 1 + 8j j = ____.

To solve for ( j ) in the equation ( 8(3j + 8) + 7 = -10 + 1 + 8j ), we can follow these steps:

1. Distribute on the left side:

[

8 cdot 3j + 8 cdot 8 + 7 = 24j + 64 + 7 = 24j + 71

]

2. Simplify the right side:

[

-10 + 1 + 8j = -9 + 8j

]

3. Set the two sides equal:

[

24j + 71 = -9 + 8j

]

4. Subtract ( 8j ) from both sides:

[

24j – 8j + 71 = -9

]

[

16j + 71 = -9

]

5. Subtract 71 from both sides:

[

16j = -9 – 71

]

[

16j = -80

]

6. Divide by 16:

[

j = frac{-80}{16} = -5

]

Thus, the solution is:

[

j = -5

]