#### Answer

$\left[ -9,\infty \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the concepts of inequalities to translate the given description, \begin{array}{l}\require{cancel}\text{ one third of a number is added to 6, giving a result of at least 3 ,}\end{array} into symbols. Then solve using the properties of inequality. Express the solution set in interval notation.
$\bf{\text{Solution Details:}}$
In symbols, the given description translates to \begin{array}{l}\require{cancel}
6+\dfrac{1}{3}x\ge3 .\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
3\left( 6+\dfrac{1}{3}x \right)\ge3(3)
\\\\
18+x\ge9
\\\\
x\ge9-18
\\\\
x\ge-9
.\end{array}
In interval notation, the solution set is $
\left[ -9,\infty \right)
.$