Question

Which of the following is an equivalent inequality?

−33>−3x−6
a) x>9
b) x<−9
c) x<−7
d) x>11

Answer 1

To find the equivalent inequality, add 3x and subtract 33 from both sides of the given inequality. Simplify and change the direction of the inequality sign to obtain the equivalent inequality. The correct answer is x > 9 (Option a).

Step-by-step explanation:

To find the equivalent inequality, we need to perform the same operations on both sides of the given inequality. In this case, we need to add 3x to both sides and then subtract 33. This gives us: 0 > -3x - 6 + 33. Simplifying further, we get: 0 > -3x + 27. To make it easier to compare, let's rewrite the inequality with the x term on the left-hand side: -3x + 27 < 0. Now, to obtain the equivalent inequality, we need to multiply both sides of the inequality by -1. This changes the direction of the inequality sign, giving us the final answer: 3x - 27 > 0. Therefore, the equivalent inequality is x > 9 (Option a).