Question

Solve these inequalities:

a) x + 14 < 4x + 2 < 3x + 11
b) x + 8 < 8x - 6 < 5x + 12

Answer 1

A) 4.7 < x < -3

B) 1.14 < x < 1.09

Explanation:

a)

x + 14 < 4x + 2 < 3x + 11

x + 14 < 4x

14 < 4x - x

14 < 3x

4.7 < x

2 < 3x + 11

2 - 11 < 3x

-9 < 3x

-3 < x

4.7 < x - 3 < x

4.7 < x < -3

b)

x + 8 < 8x - 6 < 5x + 12

x + 8 < 8x

8 < 8x - x

8 < 7x

1.14 < x

-6 < 5x + 12

12 < 5x + 6

12 < 11x

1.09 < x

1.14 < x 1.09 < x

1.14 < x < 1.09