Chapter 10 - Exponents and Radicals - 10.2 Rational Numbers as Exponents - 10.2 Exercise Set - Page 641: 105

$t=-6$

Using the Distributive Property which is given by $a(b+c)=ab+ac,$ then \begin{array}{l}\require{cancel} 2(t+3)-5=1-(6-t) \\\\ 2(t)+2(3)-5=1-1(6)-1(-t) \\\\ 2t+6-5=1-6+t .\end{array} Using the properties of equality and by combining like terms, then \begin{array}{l}\require{cancel} 2t+6-5=1-6+t \\\\ 2t-t=1-6-6+5 \\\\ t=-6 .\end{array}