3(6x+5)=2x+______x+_________

Answer 1

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

1. Distribute the 3: \[ 3(6x + 5) = 3 \cdot 6x + 3 \cdot 5 = 18x + 15. \]

So, we have: \[ 18x + 15 = 2x + ____ x + ____. \]

Next, let's rearrange the terms on the right side. We want to represent \(18x + 15\) in the form \(2x + Ax + B\), where \(A\) and \(B\) are the missing values we need to determine.

2. Combine like terms on the right side: \[ 2x + Ax + B = (2 + A)x + B. \]

To make both sides of the equation equal, we compare coefficients:

• For terms involving \(x\): \[ 18 = 2 + A. \]

  This gives: \[ A = 18 - 2 = 16. \]

• For the constant terms: \[ 15 = B. \]

Thus, we find:

• \(A = 16\)
• \(B = 15\)

Now we can fill in the blanks: \[ 3(6x + 5) = 2x + 16x + 15. \]

The completed equation is: \[ 3(6x + 5) = 2x + 16x + 15. \]