9. \( 3(2x-5)+2(4x+7)=5(3x+1) \)

Let's solve the equation step by step: \[ 3(2x - 5) + 2(4x + 7) = 5(3x + 1) \] ### Step 1: Expand the Parentheses Multiply each term inside the parentheses by the factor outside: \[ 3 \cdot 2x + 3 \cdot (-5) + 2 \cdot 4x + 2 \cdot 7 = 5 \cdot 3x + 5 \cdot 1 \] This simplifies to: \[ 6x - 15 + 8x + 14 = 15x + 5 \] ### Step 2: Combine Like Terms Combine the \(x\) terms and the constant terms on the left side: \[ (6x + 8x) + (-15 + 14) = 15x + 5 \] \[ 14x - 1 = 15x + 5 \] ### Step 3: Get All \(x\) Terms on One Side Subtract \(14x\) from both sides to get the \(x\) terms on one side: \[ 14x - 1 - 14x = 15x + 5 - 14x \] \[ -1 = x + 5 \] ### Step 4: Isolate \(x\) Subtract 5 from both sides to solve for \(x\): \[ -1 - 5 = x \] \[ -6 = x \] ### Conclusion The solution to the equation is: \[ x = -6 \]