Tutoring high school math, you might help students whose equation solving skills are rusty.  The tutor shows a technique students must know….

 
Equation solving can be like fitness. A student can be good at it, but then get out of practice. Of course, the younger students have to learn it fresh at one point.

Solving an equation with the variable, commonly x, on both sides, can be confusing at first. However, it’s easily done once you know the trick. Let’s look at an example:

Example 1: Solve -2x + 7 = 6x + 43

Solution: First, we need to “get all the x’s to one side and all the numbers to the other side.” Of course, we need to decide which side to put the x’s. While some people prefer the left, you can choose either.

In this case, I’ll choose the right side for the x’s; therefore, the numbers will need to go to the left side.

The 6x is where it needs to be, but the -2x needs to be removed from the left side. To get rid of it, we add its opposite, which is 2x, to both sides. After all, -2x+2x=0. Just remember: whatever we do to one side, we must also do to the other:

-2x +2x + 7 = 6x+2x + 43

which simplifies to

7=8x+43

Now that we’ve gotten the x’s to just the right side, we need to bring the numbers to the left. Specifically, the 43 on the right side needs to be removed. We do so by subtracting 43 from both sides:

7 -43 = 8x + 43 -43

which simplifies to

-36=8x

Finally, we need to get rid of the 8, so that just “x” sits on the right side. Since 8x means “8 times x”, we get rid of the 8 by dividing it from both sides:

-36/8=8x/8

which simplifies to

-9/2=x

Observations:

1. Lots of people would have displayed the last line as
   x=-9/2
   However, I would only write it that way if x had been on the left side before. In my case, I took the x’s to the right, so I left x there.
2. Solving high school equations, you almost never divide until the last step. Trying to do so earlier often leads to more fractions and problems.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.