# Chapter 1 - Section 1.5 - Linear Inequalities in One Variable - 1.5 Exercises - Page 101: 61

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

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

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