To solve the inequality 5x < 5 for x:
Divide both sides of the inequality by 5 to isolate x:
5x / 5 < 5 / 5
This simplifies to:
x < 1
This means that any number less than 1 satisfies the inequality.
Now, to graph the solution on a number line:
1. Draw a horizontal line and mark points on it, particularly the point corresponding to x = 1.
2. Since the inequality does not include the number 1 (it is strictly less than 1), we will use an open circle at x = 1 to indicate that 1 is not a part of the solution set.
3. Shade the region of the number line to the left of 1 to represent all numbers less than 1.
Here's a basic text representation of the number line:
```
... | ... | ... | 0 | ... | 1 | ... | ... | ...
' ' ' '
-1 0 1 2
----------------------------o------------------------->
Shaded region: <---- (Indicating all the values less than 1)
```
In the drawing above, 'o' stands for an open circle at x = 1, and the shaded region is indicated with a leftward arrow, showing all the values less than 1 are the solution to the inequality.
Solve for xx and graph the solution on the number line below.
5x<5
1 answer