## Intermediate Algebra (12th Edition)

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $10\left(\dfrac{1}{5}x+2 \right) \lt 10\left(\dfrac{1}{5}x+1 \right) ,$ use the Distributive Property and 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 Distributive Property and the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} 10\left(\dfrac{1}{5}x\right)+10(2) \lt 10\left(\dfrac{1}{5}x\right)+10(1) \\\\ 2x+20 \lt 2x+10 \\\\ 2x-2x \lt 10-20 \\\\ 0\lt-10 \text{ (FALSE)} .\end{array} Since the solution above ended with a FALSE statement, then there is $\text{ no solution .}$ There is no graph since there is no solution set.