Solving Absolute Value Inequalities (1 Viewer)

[frog1944]

Hi,

How do you solve the following types of absolute value inequalities:
1. | f(x) | > | g(x) | (whether it's >, < >=, <= doesn't matter, and where f(x) and g(x) are both functions of x, not constants)
2. 1/(| f(x) |) > 1/(| g(x) |) (same deal as above ^)

I know how to solve absolute value equations of the form | f(x) | = | g(x) | + C (constant). But inequalities I've only ever been asked and shown ones in the form of | f(x) | > g(x) + C

Thanks

 

[InteGrand]

Hi,

How do you solve the following types of absolute value inequalities:
1. | f(x) | > | g(x) | (whether it's >, < >=, <= doesn't matter, and where f(x) and g(x) are both functions of x, not constants)
2. 1/(| f(x) |) > 1/(| g(x) |) (same deal as above ^)

I know how to solve absolute value equations of the form | f(x) | = | g(x) | + C (constant). But inequalities I've only ever been asked and shown ones in the form of | f(x) | > g(x) + C

Thanks

 

[frog1944]

Thank you so much integrand