Question

Solve the inequality:

-2x > 22
Ox< 11
Ox> 11
O x>-11
O x < -11

Answer 1

Answer: x < -11

Work Shown

I'll show two methods to solving.

Method 1

-2x > 22

-2x/(-2) < 22/(-2) ........ inequality sign flip

x < -11

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Method 2

-2x > 22

-2x+2x > 22+2x

0 > 22+2x

2x+22 < 0

2x+22-22 < 0-22

2x < -22

2x/2 < -22/2 ......... no sign flip this time

x < -11

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The inequality sign flips only when dividing both sides by a negative number. The same happens when multiplying both sides by a negative number.

To graph x < -11 on a number line, follow these steps

1. Plot an open hole at -11
2. Shade to the left

The open hole means "exclude -11 from the solution set".