Quandaries and Queries


Name: davis
Who is asking: Parent
Level of the question: All

Question: 3z-5+2z=25-5z



Hi Davis,

I find it sometimes helps with a problem like this to think of the equation as a balance with the balance point at the equal sign. The object is to manipulate the terms on each side, without distorting the balance, and end with an equation of the form

z = number.

That is with the z alone on one side of the equation, and a number on the other side.

With this equation I would first gather the z-terms on the left of the equation to get

3z + 2z - 5 = 25 - 5z, which is
5z - 5 = 25 - 5z

To eliminate the z-term from the right side of the equation, add 5z to both sides. This maintains the balance and you get

5z - 5 + 5z = 25 - 5z + 5z, or
10z - 5 = 25

Now add 5 to both sides, again maintaining the balance to get

10z - 5 + 5 = 25 + 5, or
10z = 30.

Finally divide both sides by 10 to get

z = 3.