Question

What is the justification for each step in solving the inequality?

Answer 1

First step is : Distributive property, as -2 is being distributed over x and 1.

Second step: Addition property of order, because we are adding 2 to both sides  (or Subtraction: we are subtracting -2 to both sides)

Third step: Subtraction property of order, because we are subtracting 3x to both sides of the inequality.

Fourth step: Division property of order, as we are dividing both sides by -5.
(or multiplication property of order: we are multiplying both sides by -1/5

Answer 2

The given is: −2(x+1)≥3x+8
The first step is getting rid of the brackets using the distributive property.
The second and third steps is isolating the term containing the x on one side of the inequality using addition or subtraction property of order
The last step is getting rid of the coefficient of the x using the multiplication or division property of order.

So, the correct order of choices is:
1- distributive property.
2- addition or subtraction property of order
3- addition or subtraction property of order
4- multiplication or division property of order.