Question

solve the equation and check your solution.
12x + 54 = 3x
x = \boxed{}

Explanation:

Step1: Subtract $12x$ from both sides

$12x + 54 - 12x = 3x - 12x$
$54 = -9x$

Step2: Divide by $-9$ to solve for $x$

$\frac{54}{-9} = \frac{-9x}{-9}$

Step3: Verify solution in original equation

Substitute $x=-6$ into $12x + 54 = 3x$:
Left side: $12(-6) + 54 = -72 + 54 = -18$
Right side: $3(-6) = -18$
Both sides are equal, so the solution is valid.

Answer:

$-6$