What must be true? Some team members do not work with technicians
Apprentices only work with technicians
If a team member works with an apprentice, then they are a technician
No analysts work with apprentices
If a team member is not an analyst, then they work with an apprentice
a
о
30°C Mostly cloud

4 < -2x + 4 < 12

With one exception (which we'll get to), inequalities work exactly like equations.

If you had:

-2x + 4 = 12

you would have no problem solving that.

First, you would subtract 4 from both sides:

-2x = 8

Then, you would divide both sides by -2:

x = -4

No problem!

You're doing almost the same thing with inequalities. If you had a single inequality, like

-2x + 4 < 12

you would subtract 4 from both sides, same as with an equation:

-2x < 8

NOW is the only exception that comes with inequalities! WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE, YOU MUST SWITCH THE INEQUALITY SIGN. Until now, we've just left "less-than" as "less-than". Now, when we divide both sides by -2, we must change the "less-than" to a "greater-than":

x > -4

That's the only trick!

Now, with your equation, you have THREE SIDES. That might be throwing you off a bit, but don't let it! Before, you did everything to BOTH sides of an equation or inequality. Now, you do everything to ALL THREE sides. No problem!

So, you have:

-4 < -2x + 4 < 12

Start by subtracting 4, same as before. Only now you do it to all three sides:

-8 < -2x < 8

Next, you have to get rid of that -2, so you divide ALL THREE sides by -2. DON'T FORGET TO SWITCH THE SIGNS:

4 > x > -4

And you're done!

4 > x > -4

It sometimes helps to rewrite a three-part inequality as two seperate problems:

-4 < -2x + 4

-2x + 4 < 12

Don't hesitate to do this, especially for larger, messier problems! You'll get exactly the same answers!