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What is the value of y in the equation 2(3y + 7 + 5) = 196 − 16?

Group of answer choices

13

14

26

28

1 answer

Let's solve the equation step by step:

  1. Start with the equation: \[ 2(3y + 7 + 5) = 196 - 16 \]

  2. Simplify the right side: \[ 196 - 16 = 180 \] So the equation becomes: \[ 2(3y + 7 + 5) = 180 \]

  3. Simplify the expression inside the parentheses: \[ 7 + 5 = 12 \] This makes our equation: \[ 2(3y + 12) = 180 \]

  4. Divide both sides by 2: \[ 3y + 12 = 90 \]

  5. Now, isolate \(y\) by subtracting 12 from both sides: \[ 3y = 90 - 12 \] \[ 3y = 78 \]

  6. Finally, divide by 3 to solve for \(y\): \[ y = \frac{78}{3} = 26 \]

The value of \(y\) is \(26\).

Therefore, the answer is \( \boxed{26} \).