Expert: Scott A Wilson - 3/11/2010

Question
This equation totally confuses me:
5t-2(t-3)=33

I can't figure it out, although all the other problems were easy.
Can you please explain how I do the problem?

Answer
When I see 5t - 2(t-3) = 33, I immediately know that the () need to be dropped.
That is, -2*t is -2t and -2*(-3) = 6.

This gives us 5t - 2t + 6 = 33.

Next, the t's should be combined, giving 5t - 2t = (5-2)t = 3t.

We now have 3t + 6 = 33.

Now since we have an extra constant with the t's, subtract it from both sides.

This gives 3t = 33 - 6 = 27, so 3t = 27.

Now that the t's are on one side and the constant on the other, divide by the coefficient.

That is, 3t/3 = 27/3, so t = 9.

Putting this back in the original gives 5(9) - 2(9-3) = 45 - 2(6) = 45 - 12 = 33,
and that is what it is suppose to be, so we're done.