Solving inequalities?

Question

im not getting the same anwers as the book! i thought i knew how to do them but i guess not. please help!!

solve the inequality. give the result in interval notation and graph the solution set.

question 1:

-2 < -b + 3 < 5

question 2:

-6 < -3( x - 4 ) < or equal to 24

question 3:

-3( a + 2 ) > 2( a + 1 )

Answer 1

1: -2 &lt; -b +3 &lt;5

so: -b +3 &gt; -2   and -b +3 &lt; 5

     -b &gt; 1         and -b &lt; 8

divide by -1 to isolate b and the sign flips

     b &lt; -1        and b &gt;-8

the graph is like: neg. |----------8--&gt;--------(shade in here)----&lt;--1---0---|pos.

#2. -6 &lt; -3(x-4) &lt; or equal to 24

so: -3x + 12 &gt; -6 and -3x +12 &lt; or equal to 24

     -3x &gt; -18              -3x &lt; or equal to 12

      x &lt; 6                   x &gt; or equal -4

the graph is like: neg. |---------4&gt;------(shade-----0-------her... pos.

#3. -3a - 6 &gt; 2a + 2

     -5a &gt; 8

     a &lt; - 8/5

the graph is: neg. |--(shade here)---------&lt;-8/5--0--------|

i think. haha it&#039;s hard to do math on the computer, but i hope that helps a bit?

Answer 2

In the first one, subtract 3 from each amount. the one on the left, the one in the middle, and the one on the right. Then I would multiply negative one by each one, so that you can set the negative b to a positive one. Then you can see what &#039;b&#039; really is.

In the second one, solve the equation in the middle, and get rid of everything but the x in the middle. Youll have to divide everything by 3, and then subtract 4 from each one, then mult by -1 again to get to the &#039;x&#039;.

By the time you do that, you should be able to figure out the last one. Just solve for x.