Example 6 Find the mistake from the following solution.
Suppose
Þ x  3 £ 2 ....[Canceling 
x^{2}  5 from the denominator]
Þ x £ 5
Solution :
If a < b and c < 0, then ac > bc .....(I)
Since ( x^{2}  5) < 0 then
( x^{2}  5) (x^{2}  5) Þ x  3 ³ 2 ....(by I)
Þ x  3 + 3 ³ 2 + 3 \
x ³ 5
Example 7 Show that the following in equality is consistent
(3x + 15) > x + 5
Solution :
(3x + 15) > x + 5
Þ x + 5 > x + 5
The inequality is consistent
Example 8 If x + y > 0 and x < 2. Find the solution
for y
Solution :
x + y > 0 Þ 0 < x + y ....(1)
Also, x < 2 ....(2)
Adding (1) and (2) we get,
0 + x < x + y + 2
(Subtracting x from both the sides)
Þ 0 + x  x < x + y + 2  x Þ 0 < y + 2
(Subtracting 2 from both the sides)
Þ 0  2 < y + 2  2
Þ  2 < y or y >  2
Example 9
Solve
Solution :
Note that If a > 0
1)  x  = a is equal to x = a or x =  c
