Math CentralQuandaries & Queries


Question from deanna, a student:

-4x=1/5 need help with showing work and answer

Hi Deanna.

When you have an equation (that means a math expression that has at least one variable "letter" and numbers along with an equal sign in there somewhere), you want to "solve for" the variable. That means
moving things around so that the letter is on one side of the equal sign and just a number is on the other side. It doesn't matter which side (left or right) the variable is on. And the variable can be any letter, not just x.

The most important rule in algebra is this: whatever you do to one side of the equation you have to do to the other.

So let me show you how to solve this kind of question. Let's try -2 = -4z + 5.

We want z by itself. So we have to get rid of the +5 and the factor of -4 using normal math rules. Remember learning BEDMAS? Here we use it backwards! First we try to get rid of the addition (the + 5). We can get rid of the plus five by subtracting 5, because then the minus 5 cancels with plus 5. Now remember that if we subtract 5, we have to subtract 5 from BOTH sides of the equation. So now we have this:

(-2) - 5 = (-4z + 5) - 5

which is just

-7 = -4z

So z is multiplied by -4. How do we "undo" that? We can divide by -4. Then the minus fours cancel out. Again, we have to do the same thing to both sides of the equation:

(-7) / (-4) = (-4z) / (-4)

which is just

7/4 = z.

And now the problem is solved.

You can do the same kind of steps in your question to solve for x.

Hope this helps,
Stephen La Rocque.

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