#### Answer

$\left[ 3,\infty \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the concepts of inequalities to translate the given description, \begin{array}{l}\require{cancel}\text{ when $1$ is added to twice a number, the result is greater than or equal to 7 },\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} 2x+1\ge7 .\end{array}
Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel}
2x+1\ge7
\\\\
2x\ge7-1
\\\\
2x\ge6
\\\\
x\ge\dfrac{6}{2}
\\\\
x\ge3
.\end{array}
In interval notation, the solution set is $
\left[ 3,\infty \right)
.$