To solve the inequality x/3 < -2, we will follow these steps:
Step 1: Multiply both sides of the inequality by 3 (because the coefficient of x is 3 in the denominator).
3 * (x / 3) < 3 * (-2)
x < -6
So the solution to the inequality is x < -6.
To graph the solution on a number line, we will represent all the numbers less than -6. We can do this by drawing an open circle at -6 and shading the line to the left of -6.
Now let's check the solution by substituting a value less than -6 into the original inequality:
Let's pick x = -7.
Plugging x = -7 into the inequality:
(-7) / 3 < -2
Simplifying the inequality:
-7/3 is indeed less than -2.
Since the statement is true, x = -7 satisfies the inequality.
Therefore, the solution is correct.