Question

What is the solution to 3/2b + 5 < 17? Explain How.

Answer 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.

Answer 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: " $2 *\frac{3}{2}=\frac{2}{1}*\frac{3}{2}$ " } ;

Note:  To simplify:  " $\frac{2}{1} * \frac{3}{2}$ " ;
   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:  " $\frac{1}{1}*\frac{3}{1}= 1 *3 = 3$ " };

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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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