Question

The range of all real numbers x such that 2x-5 <7 and 4x+10>6 is

Answer 1

Simultaneous inequalities.

The first one gives

2x -5 < 7

2x < 5+7 = 12

x < 6

The second one

4x + 10 > 6

4x > 6 - 10 = -4

x > -1

Note we always divided by positive numbers, so the sense of the inequaltity never changed.

Our final answer is

-1 < x < 6