Solve the inequality \( 12 x<22+x \) \( x<1 / 2 \) \( x<2 \) \( x>2 \) \( x>1 / 2 \)

To solve the inequality \( 12 x < 22 + x \), we first isolate \( x \) on one side. Subtract \( x \) from both sides: \[ 12x - x < 22 \] This simplifies to: \[ 11x < 22 \] Now, divide both sides by 11: \[ x < 2 \] The correct answer is: \( x < 2 \). --- To ensure we understand how inequalities work, remember that when you multiply or divide by a negative number, you must flip the inequality sign. Also, when graphing inequalities, open circles indicate that a number is not included (like on \( x < 2 \)), whereas closed circles indicate inclusion (like on \( x \leq 2 \)). Additionally, you can always double-check your solution by picking a number below 2 (like 1) and substituting it back into the original inequality to verify that it holds true! In this case, \( 12(1) < 22 + 1 \) which simplifies to \( 12 < 23 \). Hooray for inequalities!