Question

5. If the replacement set = (-6, -3,0,3, 6, 9, 12), find the truth set of the following:
(I) 2x - 3 > 7
(ii) 3x + 8 <= 2
(iii) –3 < 1 –2x​

Answer 1

i. 2x - 3 > 7

= 2x > 7 + 3

= 2x > 10

= x > 5

= {6, 9, 12}

ii. 3x + 8 <=2

= 3x <= 2 - 8

= 3x <= -6

= x <= -2

= {-6, -3, -2} (-2 because x is less than or EQUAL TO -2)

iii. -3 < 1 - 2x

= 2x < 1 + 3

= 2x < 4

= x < 2

= {-6, -3, 0}