Question 1098127: How to do 2 step inequality equations? If im able to do this i'll get 100% on my test. Please tell me I need it right now so I can study for 2 hrs
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! You need 10 minutes for understanding,
not 2 hours for memorizing problem-solving recipes.
Solving equations and solving inequalities is very similar.
EQUAtions have an EQUAL sign, and no other sign.
Inequalities have a < or > sign,
and maybe one of those signs could be combined with an equl sign.
Both (equations and inequalities are solved the same way, with just one different detail.
FOR EQUATIONS:
To solve for x, you have to "undo" what has been doen to poor x
With the equation 3x+5=11 ,
you see that poor x was first multiplied times 3,
and then 5 was added.
To solve you "undo" what was done in reverse order.
In the morning, you put a sock first, and then a shoe on top of the sock.
Later you undo that in reverse order, taking off the shoe first.
So, to solve  , you first undo the adding 5.
If the two sides of the equal sign are equal,
subtracting 5 from both sides leaves the sides equal, so
 , which means  .
You could say that was one step.
Then you undo the multiplication times 3.
If then dividing both sides of the equal sign by 3,
you find that x equals 6 divided by 3, so  .
FOR INEQUALITIES:
With  , you could do something similar.
The inequality says  is more than  .
If you add or subtract the same thing from both sides,
the bigger side will stay bigger.
So, from , subtracting 5 from both sides,
you get  .
Then, if  is more than  ,
dividing both sides by 3, the bigger side will stay bigger,
and so you get  ,
just like if you cut each pizza in 3 equal pieces,
1/3 of a bigger pizza is more than 1/3 of a smaller pizza.
The only case where inequalities are solved differently from equations
is if you have to multiply or divide by a negative number.
I do not think you will face that difficulty at this time,
but if you multiply or divide both sides of an inequality by a negative number,
you have to flip the < or > sign.
It must be obvious to you that if  ,
multiplying both sides times  you would say  .
So from  you would get  .
"Two step inequality equations" is a name that your teacher can use to classify problems into many "types" of problems, associated with many problem solving recipes. That is a ewcipe for failure. You will memorizew the many types and the many recipes, and then will apply them the wrong way.
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