Solve the inequality for \( x \) \[ 22 \geq-7(2-x)+2 x \] Simplify your answer as much as possible.

To solve the inequality \( 22 \geq -7(2 - x) + 2x \), we will first distribute and combine like terms. 1. Distribute \(-7\): \[ -7(2 - x) = -14 + 7x \] Now, replace it in the inequality: \[ 22 \geq -14 + 7x + 2x \] 2. Combine like terms: \[ 22 \geq -14 + 9x \] 3. Add 14 to both sides: \[ 22 + 14 \geq 9x \] \[ 36 \geq 9x \] 4. Divide both sides by 9: \[ 4 \geq x \] Thus, we can write the solution as: \[ x \leq 4 \] Therefore, the solution to the inequality is \( x \leq 4 \).