Macy is painting a design that contains two repeating patterns. one pattern repeats every 8 inches. the other repeats every 12 inches. the design is 19 feet long. both patterns begin at the same place. how many times do the patterns begin in the same place?

The first time they will begin in same place is at the LCD of 8 and 12 inches  which is at  24 ins  or 2 feet.
So the total number of times  in 19 feet  = 19 / 2  = 9  - THat is 10 times if you count the point at where they start.

To solve for q, subtract 6 from both sides to undo the addition, and you will get 1/5q = 4. Then multiply each side by 5 to undo the division, and you'll end up with q=20. Also, to double check that 20 is the answer, substitute 20 in for q in the original equation, simplify, and see if both sides equal the same value, in this case both sides would equal 10.