Algebra 2 - solve the inequality..no idea?

Question

if anyone could show 1 example or explain or give answers, would be very appericiated

7. ) x + 8 < 14

8. ) -11x > 77

9. ) 2x - 1 > -5

10. ) 3x + 2 < 8

11. ) 5x - 8 > (greater than or equal to) -3

12. ) 1/2x - 1 > -5 (NO IDEA)

13. ) -x + 5 > (greater than or equal to) 6

14. ) 4 - 2x < (less than or equal to) 0

15. ) -3x + 5 > -1

16. ) 7 - 9x < 12

17. ) -5x + 1 > (greater or equal to) 1

the hardest im trying to figure out is the fraction ones like #12 & :

23. ) 3 < (less than or equal to) 1/2x - 1 < (less than or equal to) 5

25. ) 2/3x - 5 > 1

Answer 1

Think of the less than or equals sign as the same as the = sign

e.g    

7. ) x+8&lt; 14

      

      x + 8 = 14

      x + 8(- 8) = 14 (- 8)              

      x = 6        

      x + 8 &lt; 14

      x + 8(- 8) &lt; 14 (- 8)

      x &lt; 6   is your answer  

12) 1/2x - 1 &gt; -5

      1/2x -1(+ 1) &gt; -5 (+ 1)

       1/2x &gt; -4

       1/2x ( *2) &gt; -4 (*2)

         x &gt; -8      

   when the negative sign is on the x to get the negative sign to the other side, you must switch greater than to less than and vice versa

e.g. 17) -5x + 1 &gt; 1

             -5x &gt; 0

               x &lt; 0                

Answer 2

7.) x+8&lt;14

    x+8-8&lt;14-8

    x&lt;6

You try 2 single out x by doing opposite opperations and whatever you do to one side you have to do to the other (ur not going to gat an exat number)

8.)-11x&gt;77

    -11 divided by -11x&gt;77 divided by -11

   x&gt;-7

9.)2x-1&gt;-5

   2x-1+1&gt;-5+1

   2x&gt;-4

   2x/2&gt;-4/2

   x&gt;-2

I&#039;ll give u the rest tom.

g2g  

Answer 3

You use the same methods as when solving equalities.  The only difference is that when you multiply or divide by a negative number, flip the inequality.

7) x + 8 &lt; 14

Subtract 8 from each side

x = 6

8) -11x &gt; 77

Divide each side by -11

x &lt; -7  (remember to flip the inequality!!)

9) 2x = 1 &gt; -5

2x &gt; -4

x &gt; -2

10)

3x + 2 &lt; 8

3x &lt; 6

x &lt; 2

11)

5x - 8 &gt;= -3

5x &gt;= 5

x &gt;= 1

12)

1/2x - 1 &gt; -5

1/2x &gt;= 4

Multiply each side by 2!!

x &gt;= 8

13)

-x + 5 &gt;= 6

-x &gt;= 1

Multiply through by -1 and flip the inequality

x &lt;= -1

14)

4 - 2x &lt;= 0

4 &lt;= 2x

2 &lt;= x

15)

-3x + 5 &gt; -1

-3x &gt; -6

x &lt; 2

16)

7 - 9x &lt; 12

-5 &lt; 9x

-5/9 &lt; x

17)

-5x + 1 &gt;= 1

-5x &gt;= 0

x &lt;= 0

23)

3 &lt;= 1/2x - 1 &lt;= 5

Add 1 to each part

4 &lt;= 1/2x &lt;= 6

Multiply through by 2

6 &lt;= x &lt;= 12

25)

2/3x - 5 &gt; 1

2/3x &gt; 6

Divide each side by 2/3

x &gt; 9

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EDIT

I notice you have several questions, and only one has been resolved.  You should really select best answers for those that have been answered.  It&#039;s the polite thing to do, since all the answerers can get are points, and a thank you for their service.  (The thank you is more important than the points).