Question

Identify the property used in the first 5 steps to solve the equation 2(x-5)-6x=-22

Answer choices:
Step 1: Associative, Commutative or Distributive Property
Step 2: Associative, Commutative or Distributive Property
Step 3: Addition or Multiplication Property of Equality
Step 4: Addition Property or Combine Like Terms
Step 5: Addition or Multiplication Property of Equality

Answer 1

Distributive property

Explanation:

Answer 2

`2(x-5)-6x=22` ⇒ We start by multiplying out the bracket and this property is called DISTRIBUTIVE property


`2x-10-6x=-22` ⇒ from here the next step is simplifying by collecting like terms


`2x-6x-10=-22` ⇒ The simplifying process is the application of COMMUTATIVE property since this property allows us to 'group' the like terms together. In other words, this property allows us to move the
`-6x` next to the
`2x`.


`(2-6)x-10=-22` ⇒ This what actually happened when we simplify
`2x-6x`, we work out the sum of
`(2-6)` and the answer is multiplied back to
`x`. This is called the ASSOCIATIVE property as we 'associating' the constant of the like terms.


`-8x-10=-22` ⇒ Adding 10 on both sides to eliminate
`-10` on the left hand side of equation


`-8x=-22+10`

`-8x=-12`

`x= (-12)/(-8)= (3)/(2)=1.5`

Hence, the steps are

STEP 1
STEP 4
STEP 2
STEP 3
STEP 5