A carpenter has to cut a 48 inch piece of wood to fit a door, the piece of wood will fit as long as it is within a 2 inch tolerance. write out a absolute value Inequality to represent this.

So first off, lets start off with what we know:

The total sum of the angles in a triangle is always 180 degrees.

Angle A = 60 degrees. (They told us so in the picture!)

That means that:

Angle B + C = (x + 20) + 3x

And B + C = 180 - 60 = 120 degrees.

Therefore (x + 20) + 3x = 120 degrees.

So it follows that if we simplify we get:

4x + 20 = 120 degrees

4x + 20 - 20 = 120 - 20

4x = 100 degrees

x = 25 degrees.

Then we know that:

B = 3x = 3 * 25 = 75 degrees.

And:

C = x + 20 = 25 + 20 = 45 degrees.

We can check by doing:

95 + 75 + 60 = 180 degrees!

So we have solved the problem.