20 Solve \( 12 x-4=7 x+46 \)

To solve the equation \( 12x - 4 = 7x + 46 \), start by isolating the variable \( x \). First, subtract \( 7x \) from both sides: \[ 12x - 7x - 4 = 46 \] This simplifies to: \[ 5x - 4 = 46 \] Next, add \( 4 \) to both sides: \[ 5x = 50 \] Now, divide both sides by \( 5 \): \[ x = 10 \] Thus, the solution to the equation is \( x = 10 \). Now, let's check our work! Substitute \( x = 10 \) back into the original equation: Left side: \( 12(10) - 4 = 120 - 4 = 116 \) Right side: \( 7(10) + 46 = 70 + 46 = 116 \) Since both sides match, we’ve confirmed that \( x = 10 \) is indeed correct!