Question

1/7(14-7 p) - 2=-2(1/2p+3)+6 solve the equation step by step please

Answer 1

lets start with
\[\frac{1}{7}\left(14-7p\right)\] what do you get when you multiply out using the distributive law?

Answer 2

2-1p ?

Answer 3

yes, good

Answer 4

now we have on the left \[2-p-2\] or just \(-p\)

Answer 5

on the right, start with
\[-2\left(\frac{1}{2}p+3\right)\] and multiply
what do you get for this one?

Answer 6

-1p-6?

Answer 7

yup. so far so good
now what is \(-p-6+6\)?

Answer 8

-p-12?

Answer 9

not quite
what is \(-6+6\) or if you prefer \(6-6\)?

Answer 10

0

Answer 11

right, so what is \(-p-6+6\)?

Answer 12

0?

Answer 13

well actually you are left with \(-p\)

Answer 14

so on the left we removed parentheses, combined like terms, and ended up with \(-p\) and on the right the same thing happened, we also ended up with \(-p\)
now the equation looks like
\[-p=-p\]

Answer 15

oh ok so thats the answer

Answer 16

the actual answer is "this is an identity" since \(-p=-p\) is always true
in other words, both the left and right hand side of this equation are always the same, not matter what you put in for \(p\)

Answer 17

*no matter

Answer 18

Oh ok thank you very much (:

Answer 19

yw