Thread: solving inequalities

Please solve the inequalities, (the results in set notation)
1) -2 (3+x)< 4x +4 < 8x
2) [2x - 4] < 10
3) 4 < -z - 4 < 11

1. 2 < x < 5 or (2, 5)
2. x < 7 or (-inf, 7)
3. -15 < z < -8 or (-15,-8)

Originally Posted by jay1

Please solve the inequalities, (the results in set notation)
1) -2 (3+x)< 4x +4 < 8x
2) [2x - 4] < 10
3) 4 < -z - 4 < 11

1) Solve seperately: -6 - 2x < 4x + 4 and 4x + 4 < 8x:

-6 - 2x < 4x + 4 => -10 < 6x => 6x > -10 => x > -10/6.

4x + 4 < 8x => 4 < 4x => 4x > 4 => x > 1.

The answer will be the values of x common to both of these solutions.


Now try the others. If you need more help, please show your work and say where yuo get stuck.

Originally Posted by Austen Heller

1. 2 < x < 5 or (2, 5)
2. x < 7 or (-inf, 7)
3. -15 < z < -8 or (-15,-8)

The first answer is wrong - I haven't checked the others.