ShmoopTube

00:03

And here's your shmoop du jour.

00:05

Solve the inequality 23 - 2x ≥ 25 for x.

00:11

Here are the potential answers...

00:12

Before we spoil the ending, hit pause and try to solve it yourself.

00:17

OK, so, this is another two stepper.

00:19

Which adds the whole "greater than or equal to" twist.

00:22

And it can have some nasty twists, so we have to really focus every time we multiply equations

00:27

by a negative number...

00:29

...as it usually flips the "greater than" thingy around.

00:32

To solve -- for starters -- let's subtract 23 from both sides to isolate x...

00:36

...and we get that negative 2x is greater than or equal to 25 minus 23 or... 2.

00:43

Now let's just clean up x by dividing both sides by 2

00:45

and we have... negative x is greater than or equal to 1.

00:49

But now comes the twist. We have to divide both sides by negative one because we're

00:54

solving for x, not its evil twin.

00:57

Anyway, when we divide (or multiply) by a negative number, we have to flip the "greater

01:01

than" thingy so NOW we have...

01:04

...x is LESS THAN or equal to negative 1... and the answer is A.

01:08

It's worth noting that if we hadn't noticed the twist, we would have wound up with Answer B.

Full Transcript