Question

(4 - x ≤ -1) ∩ (2 + 3x ≥ 17)

Answer 1

Step-by-step answer:

Given:

two inequalities:

4-x <= -1  ........................(1)

2+3x >= 17......................(2)

Required: find the solution of the intersection of inequalities.

Solution:

Solution to (1):

4-x <= -1   transpose

4+1 <=x    simplify

5 <= x      rewrite

x >= 5

Solution to (2)

2+3x >= 17

3x >= 17-2

3x >= 15

x >= 5

The intersection of the two solutions x>=5 and x>=5 is therefore x>=5

Check:

x=4, => 4-4 = 0  >1  so not a solution

x=4, => 2+3(4) = 14 < 17 so not a solution

x=5, => 4-5 = -1  so a solution

x=5, => 2+3(5) = 17, so a solution.

similarly for 6, 7, ....