Question

solve the radical equation (sqrt of (2x+5)) < 5

Answer 1

sqrt of (2x+5) < 5

squring on each side.

2x+5 < 5^2

2x+5 < 25

Subtract 25 from each side.

2x+5-25 < 25-25

2x-20 < 0

Take common out 2.

2(x-10) < 0

Divide to each side by 2.

2(x-10)/2 < 0/2

x-10 < 0

Add 10 to each side.

x-10+10 < 0+10

x < 10

Comments

Solution of the inequality is .

Answer 2

The radical inequality

We have to solve two inequalities one with the original problem ,and one to make sure the radical in the original problem ≥ 0,Since the radical is even (Squre root).

Case 1: Solve the inequality

Squaring on each side.

Case 2: Solve the inequality

Solution two inequalities

and

Solution can be written as 

Solution .