Question

solve the following equation 5(z-4)-z=4z-20

Answer 1

expand the LHS, what do you get?

Answer 2

what does LHS stand for?

Answer 3

Hello and Welcome to OpenStudy! :)
to solve for z
first distribute the 5
can you do that?
what would you get?

Answer 4

5z-20?

Answer 5

yes :)
good!
then add like terms 5z - 20 - z = 4z - 20

Answer 6

then... oh I see why you might be confused...
ok
then if you get 0=0 (a true statement) then there are in infinite number of solutions
if you get something like 0=-20 (a false statement) then there are no solutions

Answer 7

LHS stands for Left Hand Side.

Have you added the like terms?

Answer 8

The equation has infinitely many solutions. You can write this as the solution set is the set of all real numbers. Because any number you substitute in for z will give you a true statement and thus satisfy the equation and be apart of its solution set, just like the equation y+2=2+y is true for all real numbers.