Solve and graph this inequality: 5x−2≤5 Write your solved inequality here: Should the point be open or closed?
To solve the inequality 5x-2≤5, we need to isolate the variable x on one side of the inequality. Let's do that step by step:
5x - 2 ≤ 5
First, we add 2 to both sides of the inequality:
5x - 2 + 2 ≤ 5 + 2
This simplifies to:
5x ≤ 7
Now, divide both sides of the inequality by 5:
(5x)/5 ≤ 7/5
Simplifying further:
x ≤ 7/5
Now that we have solved the inequality, we can graph it. To graph x ≤ 7/5, we start by plotting a solid (closed) point at 7/5 on the number line. Then, we shade the number line to the left from that point, as the inequality includes all values less than or equal to 7/5.
Here is the graph:
```
-inf 7/5
──●────────────
```
The point at 7/5 is represented by a closed (filled-in) circle, indicating that the value is included in the solution. The shading to the left shows all the values that satisfy the inequality.