A) What is the value of x in the equation 4(2x+1)=27+3(2x−5)4(2x+1)=27+3(2x−5)? (1 point) Responses x = 7.5 x = 7.5 x = 4 x = 4 x = 9 x = 9 x = 21 x = 21

Answer 1

To solve the equation \(4(2x + 1) = 27 + 3(2x - 5)\), we can follow these steps:

1. Distribute both sides: \[ 4(2x) + 4(1) = 27 + 3(2x) - 3(5) \] Which simplifies to: \[ 8x + 4 = 27 + 6x - 15 \]

2. Combine like terms on the right side: \[ 27 - 15 = 12 \quad \Rightarrow \quad 8x + 4 = 6x + 12 \]

3. Isolate \(x\):

   • Subtract \(6x\) from both sides: \[ 8x - 6x + 4 = 12 \] \[ 2x + 4 = 12 \]
   • Subtract \(4\) from both sides: \[ 2x = 8 \]
   • Divide by \(2\): \[ x = 4 \]

Thus, the value of \(x\) is 4.