Question

Given A = {x : -8 < 5x + 2 = 17, x belongs to I} and B = {x : -2 <= 7 + 3x < 17, x belongs to R}.

Represent A & B on two different number lines and write down the elements of A intersection B.

Answer 1

For A:

Draw a number line with a dot on 3

For B:

Draw a number line connecting points at -3 and 10/3. Open dot an 10/3, and closed dot at -3

Intersection: x = 3

Explanation:

A = {x : -8 < 5x + 2 = 17, x belongs to I}

-8 < 5x + 2 = 17

-10 < 5x = 15

-2 < x = 3

It's only x = 3

B = {x : -2 <= 7 + 3x < 17, x belongs to R}

-9《3x < 10

-3《x < 10/3

Since there's only one value in A and that also lies in B, the intersection is at x = 3