Question

7\frac{1}{3}t - \left(10\frac{2}{3}t - 6\
ight)

Explanation:

Step1: Remove the parentheses

To remove the parentheses, we distribute the negative sign to each term inside the parentheses. So, \(7\frac{1}{3}t - (10\frac{2}{3}t - 6)=7\frac{1}{3}t - 10\frac{2}{3}t + 6\)

Step2: Combine the like terms (the \(t\) terms)

First, convert the mixed numbers to improper fractions. \(7\frac{1}{3}=\frac{7\times3 + 1}{3}=\frac{22}{3}\) and \(10\frac{2}{3}=\frac{10\times3+2}{3}=\frac{32}{3}\)
Now, subtract the coefficients of \(t\): \(\frac{22}{3}t-\frac{32}{3}t=\frac{22 - 32}{3}t=\frac{- 10}{3}t=-3\frac{1}{3}t\)

Step3: Write the final expression

Combine the result from Step 2 with the constant term from Step 1. So the expression simplifies to \(-3\frac{1}{3}t + 6\)

Answer:

\(-3\frac{1}{3}t + 6\)