To match each inequality with its correct solution, follow the step-by-step explanations. For example, for 4x + 1 > 9, subtract 1 from both sides, then divide both sides by 4 to get x > 2. Repeat this process for each inequality with the corresponding signs and operations.
4x + 1 > 9: Subtract 1 from both sides to get 4x > 8. Then divide both sides by 4 to get x > 2.
-6x - 2 > 10: Add 2 to both sides to get -6x > 12. Then divide both sides by -6, remembering to reverse the inequality symbol, to get x < -2.
|3x| < 6: Remove the absolute value brackets and divide the inequality into two separate inequalities. First, solve 3x < 6 by dividing both sides by 3 to get x < 2.
Then solve -3x < 6 by dividing both sides by -3, remembering to reverse the inequality symbol, to get x > -2. The solution is -2 < x < 2.
|x+2| < 4: Remove the absolute value brackets and divide the inequality into two separate inequalities. First, solve x + 2 < 4 by subtracting 2 from both sides to get x < 2. Then solve -(x + 2) < 4 by multiplying both sides by -1 and reversing the inequality symbol to get x > -6. The solution is -6 < x < 2.
12x + 41 > 2: Subtract 41 from both sides to get 12x > -39. Then divide both sides by 12 to get x > -39/12, which simplifies to x > -13/4 or x > -3.25.
-2 < x < 2: This inequality is already solved.