Let's start by writing the sentence as an inequality. More than is the same as greater than. Therefore, x is greater than - 6.
x > - 6
or
- 6 < x
The phrase at most is the same as saying not greater than or, equivalently, less than or equal to. This means we are saying x is less than or equal to 8.
x ≤ 8
Note that the exercise uses the word and between the two inequalities. This means that we can combine the two inequalities we wrote above into a compound inequality.
First Inequality:&& -6 < x&
Second Inequality:&& x& ≤ 8
Compound Inequality:&& -6 < x& ≤ 8
To graph, we can focus on the two parts. For x > -6, we use an open circle on -6 to show that it is not included as a solution, and then we shade to the right to cover the values greater than -6. For x ≤ 8, we use a closed circle on 8 because the solution includes 8. We then shade to the left to cover the values that are less than 8.
