Consider the following rational inequality and answer the following questions:  3/2x-1 < -1

Move the -1 to the left side of the inequality

Take the denominator and multiply by the whole number and combine with the numerator

Simplify the numerator

Solve for x to find the x-intercepts and y-intercepts as ordered pairs.

Find the vertical asymptote and the horizontal asymptote
in Algebra 2 Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

3/(2x-1)<-1,

If 2x-1>0, x>½:

3<-2x+1, 2x+2<0, x<-1, in contradiction to x>½.

Therefore 2x-1<0, so x<½.

When x=½, we have

3/(2x-1)<-1,

If 2x-1>0, x>½:

3<-2x+1, 2x+2<0, x<-1, in contradiction to x>½.

Therefore 2x-1<0, so x<½.

When x=½, we have a vertical asymptote.

Also, 3>-2x+1 because -2x+1 is negative.

And 2x+2>0, x>-1.

Therefore, -1<x<½ satisfies both conditions.

When x is very large  and y=3/(2x-1)+1, the horizontal asymptote is y=1.

 

by Top Rated User (815k points)
What's the intercepts and asymptotes?

Related questions

1 answer
1 answer
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
85,994 questions
91,896 answers
2,229 comments
23,903 users