Originally Posted by

**earboth** to #1: Expand the brackets, collect all terms with the variable at the LHS of the equation:

-1/6(x-18)+1/3(x+3)=x+4 <==> -1/6x+3 + 1/3x + 1 = 4 <==>1/6x=0 <==> x = 0

to #2:

There are 2 different ways to do the question:

First transform the mixed numbers into fractions and then subtract

or

subtract integers and fractions separately:

$\displaystyle 32\frac79 - 18\frac{13}{15} = (32-18)+\left(\frac79-\frac{13}{15}\right)=14+\left(\frac{70-78}{90}\right)=14-\frac4{45} = 13\frac{41}{45}$

to #3:

You are dealing with a right triangle. Use the Pythagorean theorem. The lengths of the sides are known to you:

a = l -16

b = l - 2

c = l

Therefore:

Solve for l: $\displaystyle (l-16)^2+(l-2)^2 = l^2$

I've got x = 10 or x = 26

You have to decide which solution could be right **and why!**