(-∞, -5) ∪ (-∞, 3] plot this on a graph on the scale of -10 to +10
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.
Solve the linear inequality. Express the solution using interval notation.
8 − 3x ≤ −7
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, +∞).
To plot the set (-∞, -5) ∪ (-∞, 3] on a graph with a scale of -10 to +10, follow these steps:
Step 1: Draw the x-axis.
Step 2: Mark the points -10 and +10 on the x-axis to represent the scale.
Step 3: Draw a solid vertical line from -10 to -5 to represent the interval (-∞, -5).
Step 4: Draw a solid vertical line from -10 to 3 to represent the interval (-∞, 3].
Step 5: Shade the area between these two lines.
The graph should show a shaded area from -10 to -5, and from -10 to 3 on the x-axis.