Expert: Lynn Houston - 11/30/2008

Question
QUESTION: I've been given this question:

1) Solve the below equation.

5-x/4 = 3

My teacher says to multiply everything on the top of the fraction by 4, so would it be 20-4x = 3 ?

Please could you help me and explain.

Thanks very much.

ANSWER: No.  What you do to one side of the equality, you have to do to the other.  So, when your teacher says multiply by 4, what he means is'
4(5-x)/4 = 3(4).  On the left side, the 4s cancel, leaving 5-x = 12.  Add x to both sides and subtract 12 both sides, so you get
5-12-x+x = 12-12+x or -7 = x

So, the rules are, whatever you do to one side of the equation, you do to the other AND, to solve for the variable, you have to "undo" everything that has been done to it, so if it was multiplied by 4, you have to divide by 4, if you add 6, you have to subtract 6, etc.

---------- FOLLOW-UP ----------

QUESTION: Thanks very much. Could you help me with this other question too please:

Solve 3x-7>5 - it has inequalities in it too. Could you go through it with me please.

Thanks very, very much.

Answer
Treat it as an = sign and do the same thing (isolate the variable by "undoing" everything that has been done to it).
3x-7>5 (add 7)
3x > 12 (divide by 3)
x > 4

Check your answer by plugging a number greater than 4 into the eq and also a number less than 4.  In this case, greater than should be true and less than should be false.