How can the properties of operations be used to solve problems involving integers and rational numbers?

Properties of operations help a lot in solving problems related to integers and rational numbers.

Step-by-step explanation:

There are four properties of operations in math. These properties are applicable in case of addition and multipication but not in case of division and subtraction.

These properties are used to solve problems involving rational numbers as well as integers.These properties are associative,commutative, distributive and identity.

commutative property is A+B=B+A

                                  ⇒5+4=4+5

and                                A*B=B*A

                                  ⇒5*4=4*5

associative property ( 32+14)+7= 32+(14+7)

                                   ( 8*9)*7= 8*(9*7)

Identity property is 35+0= 35

                                    1*58=58

distributive property is 15*21

                                   ⇒  15*(20+1)

                                   ⇒15*20+15*1

                                    15*21

                                  ⇒ 15*(22-1)

                                  ⇒15*22-15*1

goog may have it for you

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.