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2(5x+6)=3x+_____x+12

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To solve the equation \( 2(5x + 6) = 3x + __x + 12 \), we first simplify the left side.

  1. Distribute the 2 on the left side: \[ 2(5x) + 2(6) = 10x + 12 \] So, we have: \[ 10x + 12 \]

  2. Now, we can rewrite the right side: \[ 3x + __x + 12 \] Let's denote the missing coefficient as \( a \): \[ 3x + ax + 12 \]

  3. Now, we set the left side equal to the right side: \[ 10x + 12 = (3 + a)x + 12 \]

  4. Since both sides have \( +12 \), we can subtract 12 from both sides: \[ 10x = (3 + a)x \]

  5. To find \( a \), we can separate the coefficients of \( x \): \[ 10 = 3 + a \]

  6. Now, solve for \( a \): \[ a = 10 - 3 = 7 \]

Now we find that the missing value in the original equation is 7, which gives us: \[ 3x + 7x + 12 \]

Thus, the complete equation reads: \[ 2(5x + 6) = 3x + 7x + 12 \]

The answer is \( 7 \).