Answer:
t = 7.5
Explanation:
The initial expression is:
[tex]\frac{3(2t-5)}{5}+2=8[/tex]Where t is the variable because is the only value that we don't know.
So, to solve for t, we need to subtract 2 from both sides:
[tex]\begin{gathered} \frac{3(2t-5)}{5}+2-2=8-2 \\ \frac{3(2t-5)}{5}=6 \end{gathered}[/tex]Multiplying by 5 in both sides:
[tex]\begin{gathered} \frac{3(2t-5)}{5}\cdot5=6\cdot5 \\ 3(2t-5)=30 \end{gathered}[/tex]Dividing by 3, we get:
[tex]\begin{gathered} \frac{3(2t-5)}{3}=\frac{30}{3} \\ 2t-5=10 \end{gathered}[/tex]Adding 5 on both sides:
[tex]\begin{gathered} 2t-5+5=10+5 \\ 2t=15 \end{gathered}[/tex]Dividing by 2, we get:
[tex]\begin{gathered} \frac{2t}{2}=\frac{15}{2} \\ t=7.5 \end{gathered}[/tex]Therefore, the solution is t = 7.5
