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?

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 : 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,

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.

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