Question

bakers work for solving (-5n - 7 = 13 + 2n) is shown. is he correct? if not, identify his mistake.
step 1: (-5n - 7 stackrel{+5n}{=} 13 + 2n)
step 2: (-7 = 13 + 2n)
step 3: (-7 stackrel{-13}{=} 13 + 2n stackrel{-13}{}
step 4: (-20 = 2n)
step 5: (\frac{-20}{2} = \frac{2n}{2})
step 6: (-10 = n)
options:

• baker is incorrect. in step 1, he should have added (5n) to both sides of the equation to preserve the addition property of equality.
• baker is incorrect. he made a mistake in step 5; instead of dividing both sides by 2 he should have subtracted 2 from both sides.
• bakers solution is correct, and i agree with his work.
• baker is incorrect. he made a mistake in step 3 when he subtracted 13 from both sides of the equation instead of adding 13 to both sides.

Explanation:

Step1: Verify Step 1 operation

Original equation: $-5n - 7 = 13 + 2n$
Add $5n$ to both sides:
$-5n - 7 + 5n = 13 + 2n + 5n$
Simplifies to: $-7 = 13 + 7n$
Baker got $-7 = 13 + 2n$, which is wrong.

Step2: Identify error source

Baker failed to add $5n$ to the right side, violating the addition property of equality (must perform the same operation on both sides to preserve equality).

Step3: Eliminate other options

• Step 3: Subtracting 13 from both sides of $-7=13+2n$ gives $-20=2n$, which is algebraically valid for that incorrect intermediate equation, so this is not the original mistake.
• Step 5: Dividing both sides of $-20=2n$ by 2 gives $n=-10$, which is valid for that incorrect intermediate equation, so this is not the mistake.
• The final solution is incorrect, so the "correct solution" option is wrong.

Answer:

Baker is incorrect. In Step 1, he should have added 5n to both sides of the equation to preserve the addition property of equality.