Question

-3x > 9.

Explain the difference between the two inequalities. How does it change one of your answers?
A) -3x > 9 represents an inequality where x is multiplied by -3, and the direction of the inequality is reversed when dividing by -3.
B) -3x > 9 and 3x > -9 are equivalent inequalities with different notation.
C) -3x > 9 and 3x > -9 are completely different inequalities with no relation.
D) -3x > 9 and 3x > -9 have the same solution set and are interchangeable.

Answer 1

The difference between the two inequalities -3x > 9 and 3x > -9 is that the direction of the inequality is reversed in the first inequality (-3x > 9) when dividing by -3. To solve each of these inequalities, we need to isolate the variable x. The solution to the first inequality is x < -3, and the solution to the second inequality is x > -3.

Step-by-step explanation:

The difference between the two inequalities -3x > 9 and 3x > -9 is that the direction of the inequality is reversed in the first inequality (-3x > 9) when dividing by -3. In the second inequality (3x > -9), the variable x is multiplied by 3, but the direction of the inequality remains the same.

To solve each of these inequalities, we need to isolate the variable x. Let's solve them step-by-step:

Inequality: -3x > 9

1. Divide both sides of the inequality by -3: -3x/-3 < 9/-3, which simplifies to x < -3.

Inequality: 3x > -9

1. Divide both sides of the inequality by 3: 3x/3 > -9/3, which simplifies to x > -3.

Therefore, the solution to the first inequality is x < -3, and the solution to the second inequality is x > -3.