Radical Functions: Solving Radical Equations and Inequalities

Example of Radical Inequality

Work through another example of solving a radical inequality.

Solve square root of the quantity two x plus one, minus three is less than zero.

 

Step 1:

2x + 1 ≥ 0
2x ≥ -1
x is greater than or equal to negative one half

Remember that the value inside the radical must be greater than or equal to zero.

Step 2:

Solve the original inequality.
Square root of the quantity two x plus one, minus three is less than zero. Square root of the quantity two x plus one is less than three. Square root of the quantity two x plus one squared is less than three squared. Two x plus one is less than nine. Two x is less than eight. x is less than 4.

Step 3:

Graph your solution on a number line to make sure that it makes sense.
x is greater than or equal to negative one half  and x < 4

x is greater than or equal to negative one half and x is less than 4. Closed dot at negative one half, open dot at four, shaded in between.