Solve the inequality below. Give the solution using interval notation. Give all values as integers or reduced fractions. (Do not convert fractions to decimals.) \( 4(x-2) \geq 2 x-4 \)

First, let's solve the inequality \( 4(x-2) \geq 2x - 4 \). Start by distributing the \( 4 \) on the left side: \[ 4x - 8 \geq 2x - 4 \] Next, isolate \( x \) by first subtracting \( 2x \) from both sides: \[ 4x - 2x - 8 \geq -4 \] This simplifies to: \[ 2x - 8 \geq -4 \] Now, add \( 8 \) to both sides: \[ 2x \geq 4 \] Finally, divide both sides by \( 2 \): \[ x \geq 2 \] In interval notation, the solution is: \[ [2, \infty) \] So, all values of \( x \) that are greater than or equal to \( 2 \) satisfy the inequality!