write the solution in interval notation

x<6 and x greater than or equal to -3

To express the solution in interval notation for the given inequality, we need to convert the inequality into a format that represents intervals on the number line.

The given inequality is:

x < 6 (x is less than 6)

This inequality represents all the values of x that are less than 6. To write this in interval notation, we use an open parenthesis to indicate that x is not included in the interval, and put the number 6 as the endpoint of the interval. So, the interval notation for x < 6 is (-∞, 6).

Now, let's consider the second part of the inequality:

x ≥ -3 (x is greater than or equal to -3)

This inequality represents all the values of x that are greater than or equal to -3. To write this in interval notation, we use a closed bracket to indicate that x is included in the interval, and put the number -3 as the endpoint of the interval. So, the interval notation for x ≥ -3 is [-3, ∞).

Now, we want to find the intersection of these two intervals to determine the values of x that satisfy both conditions. We can do this by writing the intervals side by side and taking the section where they overlap.

So, the final interval notation solution is: (-∞, 6) ∩ [-3, ∞)