2(6x+7)=2x+ ______x+14

Answer 1

To solve the equation \(2(6x + 7) = 2x + ____x + 14\), we start by simplifying the left-hand side.

1. Distributing \(2\) on the left-hand side: \[ 2(6x + 7) = 12x + 14 \]

2. Now we rewrite the equation: \[ 12x + 14 = 2x + ____x + 14 \]

3. We can simplify the right-hand side: \[ 2x + ____x + 14 = (2 + ____)x + 14 \]

4. Now we can equate the coefficients: \[ 12x = (2 + ____)x \]

5. To find the missing coefficient, we set up the equation: \[ 12 = 2 + ____ \]

6. Solving for \(____\): \[ ____ = 12 - 2 = 10 \]

Thus, the blank is filled as follows: \[ 2(6x + 7) = 2x + 10x + 14 \]

So, the complete equation is: \[ 2(6x + 7) = 2x + 10x + 14 \]

The answer is 10.