Question

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

Answer 1

$2(x-5)-6x=22$ ⇒ 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

$-8x=-22+10$
$-8x=-12$
$x= \frac{-12}{-8}= \frac{3}{2}=1.5$

Hence, the steps are

STEP 1
STEP 4
STEP 2
STEP 3
STEP 5