8) \( 3 x-3=3+4 x \)

To solve the equation \( 3x - 3 = 3 + 4x \), first, let's get all the terms involving \( x \) on one side and the constant terms on the other. Subtract \( 3x \) from both sides to get: \[ -3 = 3 + x \] Now, subtract 3 from both sides: \[ -6 = x \] Thus, the solution is \( x = -6 \). Now, to check our answer, we can substitute \( x \) back into the original equation to make sure both sides are equal: Left Side: \( 3(-6) - 3 = -18 - 3 = -21 \) Right Side: \( 3 + 4(-6) = 3 - 24 = -21 \) Both sides are equal, confirming that \( x = -6 \) is indeed the correct answer! Finding solutions to equations like this often pops up in real-world situations, such as budgeting or adjusting quantities in recipes. Balancing an equation is like balancing two sides of a scale, where you must maintain equilibrium no matter how you shift the weight! When solving similar problems, a common mistake is forgetting to perform the same operation on both sides of the equation. Always double-check: if you add, subtract, multiply, or divide one side, you must apply the same action to the other side too to keep the equation valid!