Final answer:
The equation 8u + 33 = -7(u-9) is solved by distributing the -7, combining like terms, and isolating u on one side to find that u = 2. The solution is verified by substituting back into the original equation.
Step-by-step explanation:
To solve the equation 8u + 33 = -7(u-9), first distribute the -7 across the parentheses on the right side.
- Multiply -7 by u to get -7u.
- Multiply -7 by -9 to get +63.
The equation now reads 8u + 33 = -7u + 63. Next, combine like terms by moving all terms with u to one side and constants to the other.
- Add 7u to both sides to combine the u terms: 8u + 7u + 33 = 63.
- Combine the u terms: 15u + 33 = 63.
- Subtract 33 from both sides to isolate the u term: 15u = 30.
Finally, divide both sides by 15 to solve for u: u = 2.
To check the answer, substitute u back into the original equation:
- 8(2) + 33 = -7(2 - 9)
- 16 + 33 = -7(-7)
- 49 equals 49, which confirms the solution is reasonable.