Question

solve the equation for y. -3y - 14 = 4y - 7
mr. lam, ms. claus, ms. wickstead, and mr. rodriquez solved the same problem. their work is shown below. one of their solutions is correct. next to each persons name indicate if they got it correct, and if they solved it incorrectly, indicate the error that they made. be very specific in your explanation.
mr. lam:
-3y - 14 = 4y - 7
-3y - 14 - 4y = 4y - 7 - 4y
-7y - 14 = -7
-7y - 14 + 14 = -7 + 14
-7y = 7
\frac{-7y}{-7}=\frac{7}{-7}
y = -3
correct or incorrect (circle one) if incorrect, his error:
ms. claus:
-3y - 14 = 4y - 7
-3y - 14 - 4y = 4y - 7 - 4y
-7y - 14 = -7
-7y - 14 + 14 = -7 + 14
-7y = 7
\frac{-7y}{-7}=\frac{7}{-7}
-1 = y
correct or incorrect (circle one) if incorrect, her error:
ms. wickstead:
-3y - 14 = 4y - 7
-3y - 14 + 3y = 4y - 7 + 3y
-14 = 7y - 7
-14 + 7 = 7y - 7 + 7
-7 = 7y
\frac{-7}{7}=\frac{7y}{7}
-1 = y
correct or incorrect (circle one) if incorrect, her error:
mr. rodriquez:
-3y - 14 = 4y - 7
-3y - 14 + 3y = 4y - 7 + 3y
-14 = 7y - 7
-14 + 7 = 7y - 7 + 7
-7 = 7y
\frac{-7}{7}=\frac{7y}{7}
-1.75 = y
correct or incorrect (circle one) if incorrect, his error:

Explanation:

Step1: Solve the equation \(-3y - 14=4y - 7\)

First, add \(3y\) to both sides of the equation:
\(-3y+3y - 14=4y+3y - 7\)
\(-14 = 7y-7\)
Then, add \(7\) to both sides:
\(-14 + 7=7y-7 + 7\)
\(-7=7y\)
Finally, divide both sides by \(7\):
\(y=-1\)

Step2: Check Mr. Lam's solution

Mr. Lam:
\(-3y - 14=4y - 7\)
\(-3y-14 + 3y=4y - 7+3y\)
\(-14=7y - 7\)
\(-14 + 7=7y-7 + 7\)
\(-7 = 7y\)
\(y=\frac{-7}{7}=-1\). Mr. Lam is correct.

Step3: Check Ms. Claus' solution

Ms. Claus:
\(-3y - 14=4y - 7\)
\(-3y-14+3y=4y - 7+3y\)
\(-14=7y - 7\)
\(-14+14=7y-7 + 14\) (Error: should add \(7\) to both sides, not \(14\))
Ms. Claus is incorrect.

Step4: Check Ms. Wickstead's solution

Ms. Wickstead:
\(-3y - 14=4y - 7\)
\(-3y-14+14=4y - 7+14\) (Wrong operation, should add \(3y\) first)
Ms. Wickstead is incorrect.

Step5: Check Mr. Rodriquez' solution

Mr. Rodriquez:
\(-3y - 14=4y - 7\)
\(-3y-14+3y=4y - 7+3y\)
\(-14=7y - 7\)
\(-14+7=7y-7 + 7\)
\(-7 = 7y\)
\(y=\frac{-7}{7}=-1\). But \(\frac{-7}{7}=-1
eq - 1.75\). Mr. Rodriquez is incorrect (division error).

Answer:

Mr. Lam: Correct.
Ms. Claus: Incorrect (added \(14\) instead of \(7\) to both sides).
Ms. Wickstead: Incorrect (wrong first - step operation).
Mr. Rodriquez: Incorrect (division error, \(\frac{-7}{7}=-1
eq - 1.75\)).