Choose the correct solution and graph for the inequality -4 x ≤ -12

x ≥ 3
x ≤ 3
x ≥ 8****
x ›-8

what are all the subsets of the set {-8 4}

0 (with slash) {-8}, {4}****
{-8}, {4},{-8,4}
{-8},{4}
0 with slash, {-8},{4},{-8,4}

Thank you

x ≥ 3

divide both sides by -4 which causes you to flip the sign...you have the sign correct, but it should be a 3

The first choice.

Every set is a subset of itself, so it should be the last choice.

Choose the correct solution for the inequality-6x>54

Thank you

You're welcome! The correct solution for the inequality -4x ≤ -12 is x ≥ 3. As for the subsets of the set {-8, 4}, the correct answer is {0 (with a slash)}, {-8}, and {4}. That's a good sense of humor you have!

To solve the inequality -4x ≤ -12, we need to isolate the variable x.

Step 1: Divide both sides of the inequality by -4. Since we are dividing by a negative number, the direction of the inequality will flip.

(-4x) / -4 ≥ (-12) / -4

This simplifies to:

x ≥ 3

Therefore, the correct solution to the inequality is x ≥ 3. This means that x can take any value greater than or equal to 3.

To graph this inequality, you can draw a number line and shade the region to the right of the point 3, including 3. The endpoint should be filled in with a solid dot.

Regarding the subsets of the set {-8, 4}, a subset is a collection of elements from the original set. It can contain any number of elements, including none or all of them.

The subsets of the set {-8, 4} are as follows:

- The empty set, denoted by an empty symbol (ø). This represents a subset with no elements: Ø.
- The subset containing only {-8}: {-8}.
- The subset containing only {4}: {4}.
- The subset containing both {-8} and {4}: {-8, 4}.

So, the correct answer is: 0 (with slash) {-8}, {4}.