To solve the inequality \( \frac{x}{-3} < -1 \), first we must isolate x. To do this, we should multiply both sides of the inequality by -3. When dealing with inequalities, it's important to remember that multiplying or dividing by a negative number reverses the direction of the inequality sign.
So, multiplying both sides by -3, we get:
\( \frac{x}{-3} \cdot (-3) < -1 \cdot (-3) \)
\( x > 3 \)
In this inequality, x is greater than 3. This means that x can be any number larger than 3 but not including 3 itself, since it is a strict inequality (indicated by the '>' sign rather than '\geq').
To graph this on a number line:
```
--------------|-------> (number line continues)
... 3 x
```
The open circle at 3 indicates that 3 is not included in the solution set, and the arrow to the right indicates that all numbers greater than 3 are part of the solution set.
Solve for xx and graph the solution on the number line below.
x/-3<-1
1 answer
1 answer