Question
(-∞, -5) ∪ (-∞, 3] plot this on a graph on the scale of -10 to +10
Answers
Answer
Solve the linear inequality. Express the solution using interval notation.
8 − 3x ≤ −7
8 − 3x ≤ −7
Answered by
GPT 3.5
Here is the graph of the set (-∞, -5) ∪ (-∞, 3]:
```
|--------------------------------|
-10 10
```
On this graph, the interval (-∞, -5) is represented by an open ray starting from -5 and extending indefinitely to the left. The interval (-∞, 3] is represented by a closed ray starting from 3 and extending indefinitely to the left.
```
|--------------------------------|
-10 10
```
On this graph, the interval (-∞, -5) is represented by an open ray starting from -5 and extending indefinitely to the left. The interval (-∞, 3] is represented by a closed ray starting from 3 and extending indefinitely to the left.
Answered by
GPT 3.5
To solve the linear inequality 8 - 3x ≤ -7, we can follow these steps:
Step 1: Subtract 8 from both sides of the inequality:
-3x ≤ -7 - 8
-3x ≤ -15
Step 2: Divide both sides of the inequality by -3. Note that when dividing by a negative number, we need to reverse the inequality sign:
x ≥ -15 / -3
x ≥ 5
Thus, the solution to the inequality is x ≥ 5. In interval notation, this can be expressed as [5, +∞).
Step 1: Subtract 8 from both sides of the inequality:
-3x ≤ -7 - 8
-3x ≤ -15
Step 2: Divide both sides of the inequality by -3. Note that when dividing by a negative number, we need to reverse the inequality sign:
x ≥ -15 / -3
x ≥ 5
Thus, the solution to the inequality is x ≥ 5. In interval notation, this can be expressed as [5, +∞).