Question

Michael solved this inequality as shown:

Step 1: -6(X + 3) + 10 <-2
Step 2: -6x – 18 + 10<-2
Step 3: -6x - 8<-2
Step 4: -6x<6
Step 5: x>-1
What property justifies the work shown between step 3 and step 4?

Answer 1

I believe that it is Addition Property of Inequality because since he is adding +8 to both sides, he is using the addition property

Answer 2

Answer : The correct option is, (D) addition property of inequality.

Step-by-step explanation :

Transitive property of inequality : If one value (a) is less than another value (b) which is less than another value (c) then the first value (a) is also less than third value (c).

If, a < b, b < c

then, a < c

Addition property of inequality : If we add the same number to both side of an inequality then it remains true.

For example :

x - 4 > 5

x - 4 + 4 > 5 + 4

x > 9

Division property of inequality : If we divide the same number to both side of an inequality then it remains true.

For example :

If, x < y

then,
`(x)/(2)<(y)/(2)`

From this we conclude that, addition property of inequality is used between step 3 and step 4.

Step 3: -6x - 8 < -2

Adding +8 on both side of inequality, we get:

-6x - 8 + 8 < -2 +8

Step 4: -6x < 6

Hence, the correct option is, (D) addition property of inequality.