Final answer:
To solve the equation 329=-7(1+6b), distribute -7, isolate the term with b, then divide to find b = -8. Check the solution by substituting back into the original equation to confirm it is reasonable.
Step-by-step explanation:
To solve the multi-step equation 329=-7(1+6b), first distribute the -7 across the parentheses:
-7 * 1 + (-7) * 6b = -7 - 42b
Now, the equation looks like this: 329 = -7 - 42b
Next, add 7 to both sides of the equation to isolate the terms with b:
329 + 7 = -7 + 7 - 42b
336 = -42b
After that, divide both sides by -42 to solve for b:
336 / -42 = -42b / -42
b = -8
After finding the value of b, it's important to check if the solution makes sense by substituting the value back into the original equation:
329 = -7(1 + 6(-8))
329 = -7(1 - 48)
329 = -7(-47)
329 = 329
This confirms that the solution b = -8 is reasonable and correct.