Solve the following equation, and check the solution. \( 8-2(7-2 t)=2(t-1) \)

To solve the equation \( 8-2(7-2 t)=2(t-1) \), let's first distribute the terms. Starting with the left side: 1. Distributing \(-2\) into \( (7 - 2t) \): \[ 8 - 14 + 4t = 2(t - 1) \] which simplifies to: \[ -6 + 4t = 2(t - 1) \] Now, distributing on the right side \( 2(t - 1) \): \[ -6 + 4t = 2t - 2 \] Next, let's get all \( t \) terms on one side and constants on the other: \[ 4t - 2t = -2 + 6 \] This simplifies to: \[ 2t = 4 \] Dividing both sides by 2 gives: \[ t = 2 \] Now, let's check the solution by substituting \( t = 2 \) back into the original equation: Left Side: \[ 8 - 2(7 - 2 \cdot 2) = 8 - 2(7 - 4) = 8 - 2 \cdot 3 = 8 - 6 = 2 \] Right Side: \[ 2(2 - 1) = 2 \cdot 1 = 2 \] Both sides equal 2, confirming that \( t = 2 \) is indeed the correct solution!