# x + 5 < 3 or -3x - 2 = -11

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### 3 Answers

I am assuming that this is a disjunction and, perhaps, that you are supposed to graph your results...

Both of these equations can be solved relatively simply.

For the first, you just need to subtract 5 from both sides. When you do this, you end up with

X < -2

For the second equation, you must take two steps. First, add 2 to both sides. This gets you

-3x = -9

Now, divide both sides by -3. The result is

x = -3

So now you have your answer:

x < -2 or x = -3

To solve the first inequality, you just have to keep to the left side the unknown "x" and to move the free term, 5, to the right sight, but having the negative sign.

x + 5 < 3

x < 3 - 5

**x < -2**

To solve the second equation, you also have to keep to the left side the unknown "x" and to move the free term,-2, to the right sight, but having the positive sign.

-3x - 2 = -11

-3x = -11+ 2

-3x = -9

x=-9/-3

**x=3**

**And because you used the term "or", in mathematics "or" means joining 2 sets.**

For the first inequality, where the result was x < -2, the set of x values is (-infinity, -2).

For the second equality, x={3}

Now, all we have to do is to join the both **sets:**

**X belongs** **(-infinity, -2) U {3}.**

x+5<3 or 3x-2 = -11

To detrminr the domain of x:

Solutions:

There are two constraints on x .

The set of points S to which x belongs is AUB A = {x:x+5<3},

where B = {x: -3x-2}.

A={x:x+5<3} <==> {x:x <3-5} <==>{x:x<-2}

B={x:-3x-2 = -11} <==> {x: 3x+2 = 11} <==> {x:3x =11- 2=9} <==> {x: x = 9/3 =3}

Therefore, AUB = {x: x<-2} U {x:x=3}

Therefore the domain of x is determined by the two exclusive sets {x:x<-2} or {x:x = 3}