# inequalities

1. ### Rational inequality word problem

Hi, I hope someone can help. I'm trying to understand in what cases it is okay for me to remove the denominator from a rational inequality without having to flip the inequality sign. I thought it was okay in the event that I knew that the denominator was positive. However the following word...
2. ### Solving inequalities

Hi, I hope someone can help. So I have solved the following inequality in a very specific way: I'm wondering whether there is a way to remove the denominator from a rational inequality while still providing the same solutions (i.e. -1 < x <3 or x >= 7)? All I know is that it is "bad" to...
3. ### Polynomial inequality - word problem

Hi, I hope someone can help. I'm trying to solve for the following question: <= "less than or equal to" >= "greater than or equal to" These are my steps: 1. I know that the volume of a rectangle is l x w x h - therefore the inequality to the equation must be x(50 - 2x)(30 - 2x) <= 4000...
4. ### solving inequalities algebraicly

Hi; I need to solve Y less than or equal to |x + 2| - 3. algebraicly. Thanks.
5. ### Using logarithms in a geometric distribution question involving inequalities.

The question goes like this: It is know that 9% of the population belongs to blood group B. How many people must a doctor - who is sampling random people - examine to be 99.8% confident of finding at least one person with blood group B? P(X\geqx)\leq0.002 where X = the no. of people examined...
6. ### Basic system of linear inequalities in two variables question

I just wanted to make sure that with this particular problem, the designated independent and dependent variable doesn't matter. Problem: Farmer McGregor plants oats and wheat on his farm. For conservation purposes, he plants at least twice as many acres of wheat as oats. He can handle up to a...
7. ### Having trouble with Linear Equations and Inequalities.

Hey everyone. I am having trouble with this problem and other similar problems: "In the lab, Bill has two solutions that contain alcohol and is mixing them with each other. He uses 100 mL less of solution A than solution B. Solution A is 17% alcohol and Solution B is 20% alcohol. How many mL...
8. ### Sustainable Living

A man is paid in coins $c$ starting on day $d = 0$. At the end of every week, he is paid $5$ coins. Additionally, every tenth day, he is paid $1$ coin for every tenth day since $d = 0$. The man wants to use these coins to buy as many bricks as he can so that he can build a house. Bricks cost...
9. ### Negative numbers dividing inequalities

Hi, so I have a quick question, and it's confusing me. |3x+7|>=8 So the answer is x>=1/3 and x>=-5 <--- I got that by dividing 3x by negative fifteen, now I know when you have x and it's negative you flip the signs but what if it's not x that is being divided for example: 3x+7>=-8...
10. ### Solving inequalities

Hi i am trying to solve the following but i cant figure out the last line of the solution 2x^2 \geq (x+1)^2 rearranging i get 2x^2 \geq x^2+2z+1 x^2-2x-1\geq 0 (x-1)^2 \geq 2 This is the last step given in the solution i can understand how to get to this point but i dont know where\geq2...
11. ### solving inequalities

hi, please help me to solve this inequality: 1/(3x-7) greater than or equal to 4/(3-2x) solve for the solution set (interval notation and set notation) then sketch the graph i just need to solve this but i really can't (Thinking)

16. ### Need help in dealing with fractions in Solving Systems of Linear Inequalities

I know how to graph linear inequalities and the same goes for solving 2 equations in system of linear inequalities (and do multiple shades in the graph), but when I try to solve for Y by converting into slope intercept form instead of using the intercept method to solve for both variables, the...
17. ### Inequalities

A video store has two movie-rental plans. Plan A includes a $25 membership fee plus$1.25 for each movie rental. Plan B costs \$40 for unlimited movie rentals. For what number of movie rentals is plan B less than plan A?
18. ### Inequalities

A swimming pool is 7 ft deep and is being filled at the rate of 2.5 ft per hour. How long can the pool be left unattended without the water overflowing?
19. ### Modulus and inequalities question

Given |x-2| + |x-1|>1, how do I find the values of x that satisfy this equation? I know the normal way of solving this is to square both sides, but that doesn't seem to work in this case. Thank you!
20. ### inequalities help needed

sqrt(3x^2+3x+2)-1<=sqrt(x^2-x+1) alright so this is the question, so first i set that 3x^2+3x+2=>0 and i get that x=>-1 x<=-2 for x^2-x+1 i notice it's always above zero next i do to the power of 2 on both sides and after solving what i got, i get the next boundry...