Can someone show me how to solve this inequality?

Question

Does anyone know the step by step answer to this inequality. Its not making sense to me because it is an or statement and when I graph it, the x is sandwiched between the two values. Please solve in iterval and set notation using -inf and inf for infinity. Thank you so much!

3x + 1 < 0 or 5x + 5 > −8

Answer 1

Okay, for &quot;3x + 1&lt;0&quot;.

3x +1&lt;0

     -1  -1

-------------

(the 1 cancel each other out)

it becomes:

3x &lt; -1

divide the 3 from both sides.

3/3 &lt;0/-1

3 and 3 cancel each other out.

it then becones -1/3(fraction)

the answer is x = -1/3

to check your answer you would,

3(-1/3) + 1 &lt;0

which changes to,

-1 + 1 &lt;0

Answer 2

Solve each equation separately

3x + 1 &lt; 0

3x &lt; -1

x &lt; -1/3

5x + 5 &gt; -8

5x &gt; -13

x &gt; -13/5

x&gt; -2 3/5

This give us x &lt; -1/3 OR x &gt; -2 3/5

The first is all numbers to the left of -1/3 on the number line

The second is all numbers to the right of -2 3/5 on the number line

OR means to combine the 2 sets and since -2 3/5 is to the left of -1/3 the answer is all numbers

If the problem had said AND instead of OR then you would have gotten your answer values between -1/3 and -2 3/5

Answer 3

3x+1 &lt; 0 ==&gt;  x&lt; -1/3    or   5x+5&gt; -8 ==&gt;  x&gt;-13/5

As the conjunction is or  you must take all elements of both set.

That is: all x less than -1/3 and all x greater than -13/5

In this case, as -1/3 is at right of -13/5 the set is all real numbers... that is  the interval (-infinity, + infinity)

..............................-13/5 @@@@@@@@@@@@@@@

@@@@@@@@@@@@@@@-1/3......................

The union is:

@@@@@@@@@@@@@@@@@@@@@@@@

Answer 4

3x+1&lt;0

3x+1-1&lt;0-1

3x&lt;-1

3x/3&lt;-1/3

x&lt;-1/3

and

5x+5&gt;-8

5x+5-5&gt;-8-5

5x&gt;-13

5x/5&gt;-13/5

x&gt;-13/5 sooooo;

-13/5&lt;x&lt;-1/3

ok?