Solve the inequality. Check your solutions. 7-2b<5b

Question

Solve the inequality. Check your solutions.

7−2/b<5/b

Answer 1

7 - 2/b < 5/b             First, to make our lives easier, lets multiply everything by b.

 

7b - 2 < 5                 Then we move the 2 over

 

7b < 7                     Then we divide both sides by 7

 

b < 1                       Answer.   lets check.  if we plug in a number less than b, the equation should still be correct.  let's try b = 1/2

 

7 -2/(1/2) < 5/(1/2)

 

7 -4 < 10

 

3 < 10   this equation is still correct.  so we know that value of b works.   we know for a fact that b is less than 1.  however we don't know what it's minimum is.  we know that zero doesn't work since 2/0 and 5/0 are both impossible.  what about negative numbers?  lets try b = -1

 

7 - 2/(-1) < 5/(-1)

7 +2 < -5

9 < -5   this is not true.  if you keep trying all negative numbers don't work.  even negative fractions don't work.  That said.  we can conclude that b has the domain (0,1).  Meaning that b can be anywhere number between 0 and 1.  

 

Hope that helps.  Let me know if you have any questions.

 

John