#### Answer

$t\lt\dfrac{29}{5}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
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}