Question

Simplify the expression

3(6/5p + 4q + 6) - 2(9/5p + 8q + 3)
A. -4Q +12

B. 2/5p - 4Q +12

C. 28Q +12

D. 28Q +24

Answer 1

A. -4q+12 sorry it’s it’s wrong

Answer 2

We conclude that:

`(18p)/(5)+12q+18-(18p)/(5)-16q-6=-4q+12`

Hence, option A is true.

Explanation:

Given the expression

`3\left((6)/(5)p+4q+6\right)-2\left((9)/(5)p+8q+3\right)`

solving the expression

`3\left((6)/(5)p\:+\:4q\:+\:6\right)\:-\:2\left((9)/(5)p\:+\:8q\:+\:3\right)=3\left((6p)/(5)+4q+6\right)-2\left((9p)/(5)+8q+3\right)`

Expand
`3\left((6p)/(5)+4q+6\right)=(18p)/(5)+12q+18`

`=(18p)/(5)+12q+18-2\left((9p)/(5)+8q+3\right)`

Expand
`-2\left((9p)/(5)+8q+3\right)=-(18p)/(5)-16q-6`

`=(18p)/(5)+12q+18-(18p)/(5)-16q-6`

Group like terms:

`=(18p)/(5)-(18p)/(5)+12q-16q+18-6`

Add similar elements:
`(18p)/(5)-(18p)/(5)=0`

`=12q-16q+18-6`

Add similar elements: 12q-16q=-4q

`=-4q+18-6`

`=-4q+12`

Therefore, we conclude that:

`(18p)/(5)+12q+18-(18p)/(5)-16q-6=-4q+12`

Hence, option A is true.