4/(x+5) < 1/(2x+3); solve for x

Question

4/(x+5) < 1/(2x+3); solve for x

Answer 1

4/(x+5) < 1/(2x+3)

 

4/(x+5) - 1/(2x+3) < 0

 

[4(2x+3) - (x+5)]/[(x+5)(2x+3)] < 0

 

(7x +7)/[(x+5)(2x+3)] < 0

 

Numerator = 0 when x = -1

Denominator = 0 when x = -5 or x = -3/2

 

When x < -5, (7x+7)/[(x+5)(2x+3)] < 0

When -5<x<-3/2, (7x+7)/[(x+5)(2x+3)] > 0

When -3/2<x<-1, (7x+7)/[(x+5)(2x+3)] < 0

When x > -1, (7x+7)[(x+5)(2x+3) > 0

 

Solution set:  (-∞, -5) ∪ (-3/2, -1)

 

 

 

 

Answer 2

4/(X+5) < 1/(2X+3)

 

FIRST MULTIPLY BOTH SIDES BY (X+5), AND THEN (2X+3)

THIS IS THE EQUIVALENT OF CROSS MULTIPLYING    

 

4(2X+3) < X+5       OR    8X + 12  <  X + 5

 

NOW SUBT X FROM EACH SIDE, AND SUBT 12 FROM EACH SIDE

 

7X  <  -7       OR   X  < -1