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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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.