Question

Micheal 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 4?

Answer 1

Answer: addition property of inequality

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Step-by-step explanation:

These are the steps to focus on

step 3: -6x - 8 < -2

step 4: -6x < 6

The move from the third step to the fourth step has us adding 8 to both sides. Therefore, we use the addition property of inequality.

That property has four forms

1. If
   `a > b` then
   `a + c > b+c`
2. If
   `a < b` then
   `a+c < b+c`
3. If
   `a \ge b` then
   `a + c \ge b+c`
4. If
   `a \le b` then
   `a+c \le b+c`

It's similar to the idea of starting with a = b, then adding c to both sides to get a+c = b+c

We add the same thing to both sides to keep things balanced.