2/3 + 1/2 (x+10)+ 4/5= ?

Question

Please explain step by step..

I know how to solve the simple equations... but this one confuses me.

& Explain to me what Commutative & Associative property is..

Thanks :)

Answer 1

first get rid of the parenthesis so:

2/3 + x/2 + 5 + 4/5 = ?

now combine like terms:

(x/2) + (2/3 + 4/5 + 5) = ?

(x/2) + (10/15 + 12/15 + 75/15 = ?  [did least common denom]

(x/2) + (97/15) = ?

now algebra, ill assume you mean ? = 0 bc there is a variable and the right side must equal something

x/2 = -97/15

x = -97/30

Answer 2

They are the properties that let you open the parenthesis

example: you cant solve x+10 so you have to get rid of the parenthesis

to do that you multiply the # before the parenthesis by the #'s inside

1/2*x and 1/2*10=1/2+5

Answer 3

2/3 + 1/2 (x + 10) + 4/5

2/3 + 1/2x + 1/2*10 +4/5

2/3 + 1/2x + 5 + 4/5

1/2x + 97/15

1/2x or 6.4666

Answer 4

Commutative Law (CL): a+b=b+a, i.e. I can switch them around.

Associative Law (AL): a + (b + c) = (a + b) + c, i.e. I can start by adding the last two first or I can start by adding the first two.

1/2 (x +10) + 2/3 + 4/5 = 0 (CL)

1/2 (x +10) + (2/3 + 4/5) = 0 (AL)

1/2 (x +10) + (22/15) = 0

1/2 (x +10) = -22/15

(x + 10) = -44/15

x = -10 - 44/15 = -12 14/15

Answer 5

Commutative property is when terms move around

a + b = b + a  

It's like when you commute back and forth to school.  You travel the same distance both ways so driving from school to home is an equal distance as from home to school.

Associative property : (a + b) + c = a + ( b + c)

It's like when you associate with different friends at school.  First a chats with b, and friend c is on the outside.  But soon b chats with c and a is on the outside and that's ok too.

2/3 + 1/2 (x+10)+ 4/5

2/3 + 1/2x + 1/2*10 + 4/5

2/3 + 1/2x + 5 + 4/5

1/2x + 97/15

OR 1/2x + 6.466666666666

Good luck to you !!