Question

Help.? please, i dont understand.

Answer 1

Answer: Choice B

Filled in circle at -1; shading to the right

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Step-by-step explanation:

Let's isolate x

`-3x+12 \le 15\\\\-3x+12-12 \le 15-12\\\\-3x \le 3\\\\(-3x)/(-3) \ge (3)/(-3) \ \text{ note the inequality sign flip}\\\\x \ge -1\\\\`

We solve this as if this was an equation, though the inequality sign flips when we divide both sides by a negative value (in the second to last step).

To isolate x, we undo the order of operations PEMDAS. So we first undo the "+12" by subtracting 12 from both sides (step 2). After that we undo the multiplication by dividing both sides by -3.

The graph of
`x \ge -1` will have a closed or filled in circle at -1, and shading to the right. This visually represents the solution set "x is -1 or larger". The reason why we have a filled in circle is to include the endpoint due to the "or equal to" as part of the inequality sign.

Answer 2

B

Step-by-step explanation:

Given

- 3x + 12 ≤ 15 ( subtract 12 from both sides )

- 3x ≤ 3

Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity.

x ≥ - 1

Since x can equal - 1, we are looking for a solid circle at x = - 1 on the number line.

Since x greater than - 1 we require the shaded arrow to be pointing right.

Graph B represents this