Question

Drag the tiles to the boxes to form correct pairs. Match the pairs of equivalent expressions.

Answer 1

Answer with explanation:

a)

$(4t-\dfrac{8}{5})-(3-\dfrac{4}{3}t)$

On opening the parentheses term we get:

$4t-\dfrac{8}{5}-3+\dfrac{4}{3}t$

On combining the like terms:

$4t+\dfrac{4}{3}t-\dfrac{8}{5}-3$

$=\dfrac{4t\times 3+4t}{3}-\dfrac{8+3\times 5}{5}\\\\\\=\dfrac{12t+4t}{3}-\dfrac{8+15}{5}\\\\=\dfrac{16t}{3}-\dfrac{23}{5}$

b)

$5(2t+1)+(-7t+28)$

on using the distributive property for the first terms and opening the parentheses for the second term we have:

$5\times 2t+5\times 1-7t+28\\\\=10t+5-7t+28\\\\=10t-7t+5+28\\\\=3t+33$

c)

$(-\dfrac{9}{2}t+3)+(\dfrac{7}{4}t+33)$

On combing the like terms we have:

$-\dfrac{9}{2}t+\dfrac{7}{4}t+3+33\\\\=\dfrac{-9t\times 2+7t}{4}+36\\\\\\=\dfrac{-18t+7t}{4}+36\\\\\\=\dfrac{-11t}{4}+36$

d)

$3(3t-4)-(2t+10)$

on using the distributive property for the first terms and opening the parentheses for the second term we have:

$=3\times 3t+3\times (-4)-2t-10\\\\\\=9t-12-2t-10$

Now, on combining the like terms we have:

$=9t-2t-12-10\\\\=7t-22$

Answer 2

Answer:

Step-by-step explanation:

look this solution