Answers

1. 3/2b + 5 < 17

   We subtract 5 from both sides of the inequality.

   3/2b + 5 – 5 < 17 – 5

   3/2 b < 12

   Multiply both sides by 2/3.

   ( 2/3) * (3/2b) < (2/3) * 12

   b < 8

   Therefore, the correct option is alternative “A”.

   We would think that it is option B, but the only difference is that it changes the direction of the sign.

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2. Answer:  [A]: ” b < 8 ” .
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   Step-by-step explanation:

   Given:
   Find the solution to:   ” 3/2b + 5 < 17 ” ; and choose from the answer choices.

   So; we have:  

    (3/2)b + 5 < 17  ;

    Now, subtract “5” from each side of this inequality:
    (3/2)b + 5 − 5  <  17 − 5  ;

      To get:
     (3/2)b  <  12 ;

   Now, let’s multiply Each Side of this inequality by “2” ;

    to get rid of the fraction:

       ”  2*(3/2)b  <   12*2 ”  ;

   {Note: ” ” } ;

   Note:  To simplify:  ” ” ;
      Note the “2” in the denominator in the “first term” ;  

      And:  The “2” in the denominator in the “second term” ;

         Both “cancel out” to “1” ;  since:  “[ 2 / 2 = 2÷2 = 1 ]” ;

      And:  we have:  ” ” };

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   and rewrite:
      ” 3b < 24 ”  ;

   Now, divide Each side of the inequality by “3” ;

    to isolate “b” on one side of the inequality;

   and to solve for “x” ;
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    ” 3b/3 < 24/3 ” ;

    to get:

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      “ b < 8 ” ; which corresponds to the correct answer:

   Answer choice:  [A]:  ” b < 8 ” .
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   Hope this is helpful to you! Best wishes!
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