Questions: Solve the equation. Be sure to check your proposed solution by substituting it for the variable in the original equation. 4(3x-8)-2=4(x-2)+14 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is . (Type an integer or a simplified fraction.) B. The solution set is x x is a real number . C. The solution set is ∅.

Solution Steps

To solve the equation \(4(3x - 8) - 2 = 4(x - 2) + 14\), we will first expand both sides of the equation. Then, we will collect like terms and isolate the variable \(x\) on one side of the equation. Finally, we will solve for \(x\) and verify the solution by substituting it back into the original equation.

We start with the equation: \[ 4(3x - 8) - 2 = 4(x - 2) + 14 \] Expanding both sides gives: \[ 12x - 32 - 2 = 4x - 8 + 14 \] This simplifies to: \[ 12x - 34 = 4x + 6 \]

Next, we isolate \(x\) by moving all terms involving \(x\) to one side and constant terms to the other: \[ 12x - 4x = 6 + 34 \] This simplifies to: \[ 8x = 40 \]

Dividing both sides by 8 gives: \[ x = \frac{40}{8} = 5 \]

To verify, we substitute \(x = 5\) back into the original equation: \[ 4(3(5) - 8) - 2 = 4(5 - 2) + 14 \] Calculating both sides: Left side: \[ 4(15 - 8) - 2 = 4(7) - 2 = 28 - 2 = 26 \] Right side: \[ 4(3) + 14 = 12 + 14 = 26 \] Since both sides are equal, the solution is verified.

Final Answer