# Chapter 1 - Section 1.5 - Linear Inequalities in One Variable - 1.5 Exercises: 25

$\left[ \dfrac{1}{2},\infty \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $6x-4\ge-2x ,$ use the properties of inequality. For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$ For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$ $\bf{\text{Solution Details:}}$ Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} 6x+2x\ge4 \\\\ 8x\ge4 \\\\ x\ge\dfrac{4}{8} \\\\ x\ge\dfrac{1}{2} .\end{array} The red graph is the graph of the solution set. In interval notation, the solution set is $\left[ \dfrac{1}{2},\infty \right) .$

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