Answer:
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
Answer: Choice B
Filled in circle at -1; shading to the right
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Explanation:
Let's isolate x
[tex]-3x+12 \le 15\\\\-3x+12-12 \le 15-12\\\\-3x \le 3\\\\\frac{-3x}{-3} \ge \frac{3}{-3} \ \text{ note the inequality sign flip}\\\\x \ge -1\\\\[/tex]
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 [tex]x \ge -1[/tex] 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.
