## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$t\lt\dfrac{29}{5}$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $5(t-3)+4t\lt2(7+2t) ,$ use the Distributive Property and the properties of inequality to isolate the variable. $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the inequality above is equivalent to \begin{array}{l}\require{cancel} 5(t-3)+4t\lt2(7+2t) \\\\ 5(t)+5(-3)+4t\lt2(7)+2(2t) \\\\ 5t-15+4t\lt14+4t .\end{array} Using the properties of inequality to isolate the variable, then \begin{array}{l}\require{cancel} 5t-15+4t\lt14+4t \\\\ 5t+4t-4t\lt14+15 \\\\ 5t\lt29 \\\\ t\lt\dfrac{29}{5} .\end{array}