Answer
$t=\dfrac{5}{3}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
0.76+0.21t=0.96t-0.49
,$ remove first the decimal numbers by multiplying both sides by a power of $10.$ Then use the properties of equality to isolate the variable. Do checking of the solution.
$\bf{\text{Solution Details:}}$
Since the largest number of decimal places a term has is $2,$ multiply both sides by $100.$ This results to
\begin{array}{l}\require{cancel}
0.76+0.21t=0.96t-0.49
\\\\
100(0.76+0.21t)=100(0.96t-0.49)
\\\\
76+21t=96t-49
.\end{array}
Using the properties of equality to isolate the variable, the equation above is equivalent to
\begin{array}{l}\require{cancel}
76+21t=96t-49
\\\\
21t-96t=-49-76
\\\\
-75t=-125
\\\\
t=\dfrac{-125}{-75}
\\\\
t=\dfrac{\cancel{-25}(5)}{\cancel{-25}(3)}
\\\\
t=\dfrac{5}{3}
.\end{array}
Checking: If $t=\dfrac{5}{3},$ then
\begin{array}{l}\require{cancel}
0.76+0.21t=0.96t-0.49
\\\\
0.76+0.21\left( \dfrac{5}{3} \right) =0.96\left( \dfrac{5}{3} \right) -0.49
\\\\
0.76+0.35 =1.6-0.49
\\\\
1.11 =1.11
\text{ (TRUE) }
.\end{array}
Hence, the solution is $
t=\dfrac{5}{3}
.$
