Mary Ann solves the inequality −3x≥12. Justify the steps Mary Ann takes to find the solution set.(1 point)
Responses
A. Mary Ann divides both sides of the inequality by −3 to get x≥−4.
B. Mary Ann adds −3 to both sides of the inequality to get x≥9.
C. Mary Ann adds −3 to both sides of the inequality and changes the inequality symbol to ≤ to get x≤9.
D.
Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ to get x≤−4.
The correct answer is A. Mary Ann divides both sides of the inequality by -3 to get x≥-4.
To solve the inequality -3x≥12, Mary Ann needs to isolate the variable x. Dividing both sides of the inequality by -3 will eliminate the coefficient in front of x. When dividing both sides by a negative number, the inequality sign flips.
Thus, dividing both sides by -3 results in x≥-4. This is the correct solution set for the given inequality.
, the inequality sign flips.
thus
D
x </= -4
try x = -5
−3x * (-5 )≥12
sure enough +15 > 12
Apologies for the confusion in the initial response. You are correct, the correct answer is D. Mary Ann divides both sides of the inequality by -3 and changes the inequality symbol to ≤ to get x≤-4.
When dividing both sides of the inequality by a negative number, the inequality sign should be flipped. Therefore, when -3x≥12 is divided by -3, the inequality sign changes to ≤.
Thus, the correct solution set for the inequality -3x≥12 is x≤-4. This means that any value of x that is less than or equal to -4 satisfies the inequality. For example, if we substitute x=-5 into the inequality, we get -3(-5)≥12, which is true.
The correct answer is D. Mary Ann divides both sides of the inequality by -3 and changes the inequality symbol to ≤ to get x≤-4.
Here's a step-by-step explanation of Mary Ann's process:
1. Start with the inequality: -3x ≥ 12
2. To isolate x, divide both sides of the inequality by -3. However, when dividing or multiplying an inequality by a negative number, the direction of the inequality symbol must be flipped. So dividing both sides by -3 gives us: x ≤ -4
Therefore, Mary Ann divides both sides of the inequality by -3 and changes the inequality symbol to ≤ to get x ≤ -4.