To solve each inequality and match it with its correct solution, perform the necessary operations to isolate the variable x. Remember to reverse the inequality sign when dividing or multiplying by a negative number. The matches are: 4x + 1 > 9: x > 2, -6x - 2 > 10: x < -2/3, |3x| < 6: -2 < x < 2, x + 2 < 41: x < 39, 12x + 41 > 2: x > -13/4
To solve each inequality and match it with its correct solution:
4x + 1 > 9: Subtract 1 from both sides and then divide both sides by 4 to get x > 2.
-6x - 2 > 10: Add 2 to both sides and then divide both sides by -6. Remember to reverse the inequality sign since we're dividing by a negative number. The solution is x < -2/3.
|3x| < 6: Solve for both the positive and negative cases:
Positive case: 3x < 6. Divide both sides by 3 to get x < 2.
Negative case: -3x < 6. Divide both sides by -3, and reverse the inequality sign to get x > -2.
The solution is -2 < x < 2.
x + 2 < 41: Subtract 2 from both sides to get x < 39.
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.
The matches are:
4x + 1 > 9: x > 2
-6x - 2 > 10: x < -2/3
|3x| < 6: -2 < x < 2
x + 2 < 41: x < 39
12x + 41 > 2: x > -13/4