Inequalities question?

Question

'Given that 4x > 1 and x/3 <= 1 1/3,

Find possible integer values of x' (<= means less than or equal to)

Please can you explain how to do this.

Thanks!!

Answer 1

First part, treat it as you would an equation, so:
4x >1
so divide both sides by 4
x > 1/4

2nd part
x/3 <= 1 1/3
so multiply both sides by 4
x <= 4

We now know that x > 1/4 and <= 4 meaning that the integer values it can be are:

1,2,3 and 4

Answer 2

4x > 1 and x/3 <= 1 1/3
x > (1/4) and x <= (1 1/3)*3 = 4

Since (1/4) < x <= 4, so the possible integers are 1, 2, 3, 4.

Answer 3

The answer is any number equal to or less than 4. (1,2,3 or 4)Concentrate on the second equation 1 1/3*3 = 4 and as 1 1/3 is the highest you can go that is all the answers can be and as long as your answer is above 0.25 then it fits the first equation as well.

Answer 4

4x > 1 and x/3 <= 1 1/3
x > 1/4 and x <= 4/3 * 3
x > 1/4 and x <= 4
Solution: {x belongs to R | 1/4 ::

Answer 5

1 1/3 = 1+1/3
You need to keep x on one side and all other number to the other:

FIRST INEQUALITY:
4x>1 therefore x>1/4 (multiplication becomes division when you bring it over the arrow and vice versa)
SECOND ONE:
x/3<= 1 1/3 therefore x<= 3 (1 1/3) = 3 3/3 = 4 (Division becomes multiplication when you bring it over the arrow)
or x<=4

Then put the two together (with the correct direction of arrows):
1/4< x <= 4 , so x=1,2,3,4.