Simplify $(22a+60b)+(10a+29b)-(9a+50b).$
To simplify this expression, I need to combine like terms by adding or subtracting the coefficients of the same variable. I can use the distributive property to rewrite the expression as $22a+60b+10a+29b-9a-50b$. Now I can rearrange the terms so that the ones with the same variable are next to each other: $22a+10a-9a+60b+29b-50b$. Then I can add or subtract the coefficients of each variable: $(22+10-9)a+(60+29-50)b$. This simplifies to $23a+39b$. 