Question

2
select the correct answer.
consider the following equation.
12w - 27 = -34 + 14w
which equation has the same solution as the given equation above?
a. $-\frac{1}{6}w + 2 = \frac{11}{3} - \frac{1}{6}w$
b. $-2w + 21 = -8w + 36$
c. $-47 - 10w = -9w - 40 - 3w$
d. $\frac{9}{7}w = \frac{13}{14}w + 2$

Explanation:

Step1: Solve the given equation

Given equation: \(12w - 27=-34 + 14w\)
Subtract \(12w\) from both sides: \(-27=-34 + 2w\)
Add 34 to both sides: \(7 = 2w\)
Divide by 2: \(w=\frac{7}{2}=3.5\)

Step2: Solve option A

Equation: \(-\frac{1}{6}w + 2=\frac{11}{3}-\frac{1}{6}w\)
Add \(\frac{1}{6}w\) to both sides: \(2=\frac{11}{3}\) (False, no solution)

Step3: Solve option B

Equation: \(-2w + 21=-8w + 36\)
Add \(8w\) to both sides: \(6w + 21 = 36\)
Subtract 21: \(6w=15\)
Divide by 6: \(w=\frac{15}{6}=2.5\) (Not equal to 3.5)

Step4: Solve option C

Equation: \(-47-10w=-9w - 40-3w\)
Simplify right side: \(-47-10w=-12w - 40\)
Add \(12w\) to both sides: \(-47 + 2w=-40\)
Add 47: \(2w = 7\)
Divide by 2: \(w=\frac{7}{2}=3.5\) (Matches the solution)

Step5: Solve option D (for verification)

Equation: \(\frac{9}{7}w=\frac{13}{14}w + 2\)
Multiply by 14: \(18w = 13w+28\)
Subtract 13w: \(5w = 28\)
\(w=\frac{28}{5}=5.6\) (Not equal to 3.5)

Answer:

C. \(-47 - 10w = -9w - 40 - 3w\)