Answer with explanation:
a)
[tex](4t-\dfrac{8}{5})-(3-\dfrac{4}{3}t)[/tex]
On opening the parentheses term we get:
[tex]4t-\dfrac{8}{5}-3+\dfrac{4}{3}t[/tex]
On combining the like terms:
[tex]4t+\dfrac{4}{3}t-\dfrac{8}{5}-3[/tex]
[tex]=\dfrac{4t\times 3+4t}{3}-\dfrac{8+3\times 5}{5}\\\\\\=\dfrac{12t+4t}{3}-\dfrac{8+15}{5}\\\\=\dfrac{16t}{3}-\dfrac{23}{5}[/tex]
b)
[tex]5(2t+1)+(-7t+28)[/tex]
on using the distributive property for the first terms and opening the parentheses for the second term we have:
[tex]5\times 2t+5\times 1-7t+28\\\\=10t+5-7t+28\\\\=10t-7t+5+28\\\\=3t+33[/tex]
c)
[tex](-\dfrac{9}{2}t+3)+(\dfrac{7}{4}t+33)[/tex]
On combing the like terms we have:
[tex]-\dfrac{9}{2}t+\dfrac{7}{4}t+3+33\\\\=\dfrac{-9t\times 2+7t}{4}+36\\\\\\=\dfrac{-18t+7t}{4}+36\\\\\\=\dfrac{-11t}{4}+36[/tex]
d)
[tex]3(3t-4)-(2t+10)[/tex]
on using the distributive property for the first terms and opening the parentheses for the second term we have:
[tex]=3\times 3t+3\times (-4)-2t-10\\\\\\=9t-12-2t-10[/tex]
Now, on combining the like terms we have:
[tex]=9t-2t-12-10\\\\=7t-22[/tex]
