Question

Consider the inequality 2x+3 greater than or equal to -3. Find the set of all integer solutions of this inequality that are also solutions of the inequality 5x-2<3

Answer 1

Explanation:

First we need the find the set of x such as 2x + 3 >= -3

2x + 3 >= -3 [Sum -3 in both sides]

2x + 3 - 3 >= - 3 - 3

2x >= -6 [Now, divide both sides by 2]

2x / 2 >= -6/2

x >= - 3

So, for every x>= -3 we have that 2x + 3 >= -3

Now we do the same with the other ineq:

5x-2 < 3 [sum 2 in both sides]

5x - 2 + 2 < 3 + 2

5x < 5 [divide by 5 in both sides]

5x / 5 < 5 / 5

x < 1

So, for every x<1 we have 5x-2<3

Then our set it the intersection of both of the previous sects, it is:

(x<1)intersect(x>=-3):

Solution: -3 =< x < 1