# Math Help - Solving ineqality problem

1. ## Solving ineqality problem

given that (4x/5)-(1/10)<=x-(2/5), state the smallest value of x when

1)x is an integer

2)x is prime number

3)x is a rational number

please guide me on how should i solve these ?

2. ## Re: Solving ineqality problem

Start by solving the inequality...

3. ## Re: Solving ineqality problem

but what should i do then ?

4. ## Re: Solving ineqality problem

Originally Posted by haftakhan

but what should i do then ?
I don't get $\displaystyle 4.5 \leq x$...

\displaystyle \begin{align*} \frac{4x}{5} - \frac{1}{10} &\leq x - \frac{2}{5} \\ \frac{4x}{5} + \frac{3}{10} &\leq x \\ \frac{3}{10} &\leq \frac{x}{5} \\ \frac{3}{2} &\leq x \end{align*}

What is the smallest integer which satisfies this inequality? What is the smallest prime number? What is the smallest rational number?

5. ## Re: Solving ineqality problem

How u get 3/10 after solving (-1/10)+(2/5) ?

6. ## Re: Solving ineqality problem

$\displaystyle -\frac{1}{10} + \frac{2}{5} = -\frac{1}{10} + \frac{4}{10} = \frac{3}{10}$

7. ## Re: Solving ineqality problem

Integer is 1

Prime number will be 1 as well

Rational number ???

8. ## Re: Solving ineqality problem

Originally Posted by haftakhan
Prime number will be 1 as well
The number 1 is not prime.
If you do not know that, you should not attempt this question.
Moreover, anyone asked to do this question surely knows what a rational number is.

9. ## Re: Solving ineqality problem

Originally Posted by haftakhan
Integer is 1

Prime number will be 1 as well

Rational number ???
For that matter 1 is also smaller than 3/2 so it doesn't satisfy the inequality

10. ## Re: Solving ineqality problem

Sorry ,i thought x was lesser than 3/2

integer and prime number should be 2

11. ## Re: Solving ineqality problem

Originally Posted by haftakhan
Sorry ,i thought x was lesser than 3/2

integer and prime number should be 2
Okay, and your condition was that $x\ge \frac{3}{2}$. What is the smallest rational number satifying that?

12. ## Re: Solving ineqality problem

It would be 3/2

13. ## Re: Solving ineqality problem

Originally Posted by haftakhan
It would be 3/2
Correct.

14. ## Re: Solving ineqality problem

Yes, e^ipi, he said that in post #10.