Question

1. $8.2t + 5.1(t + 3) - 6(2t - 4)$

Explanation:

Step1: Expand the brackets

First, we expand \(5.1(t + 3)\) and \(-6(2t - 4)\) using the distributive property \(a(b + c)=ab+ac\).
For \(5.1(t + 3)\), we get \(5.1t+5.1\times3 = 5.1t + 15.3\).
For \(-6(2t - 4)\), we get \(-6\times2t-6\times(- 4)=-12t + 24\).
So the expression becomes \(8.2t+5.1t + 15.3-12t + 24\).

Step2: Combine like terms

Now we combine the terms with \(t\) and the constant terms separately.
The terms with \(t\) are \(8.2t\), \(5.1t\) and \(-12t\).
\(8.2t+5.1t-12t=(8.2 + 5.1-12)t=(13.3 - 12)t = 1.3t\).
The constant terms are \(15.3\) and \(24\).
\(15.3+24 = 39.3\).

So the simplified expression is \(1.3t+39.3\).

Answer:

\(1.3t + 39.3\)