Solve using the multiplication principle and then graph -13x>-65
To solve the inequality -13x > -65 using the multiplication principle, we need to divide both sides of the inequality by -13. However, when dividing or multiplying both sides of an inequality by a negative number, we need to reverse the direction of the inequality symbol.
So, dividing both sides by -13, we have:
x < -65 / -13
Simplifying the right side, we get:
x < 5
This means that x is any value less than 5.
To graph this inequality on a number line, we represent all values of x less than 5. We can do this by starting a number line at 5 and shading to the left side of the number line. In this case, since x is less than 5 but not equal to 5, we use an open circle at 5 to indicate that it is not included in the solution.
Here is the graph:
```
<---|---|---|---|---(5)---|---|---|---|--->
```
The shaded area represents all values of x that satisfy the inequality -13x > -65, which is x < 5.