On Monday, we looked at solving an equation where the variable was on one side of the equation. Today, we’re going to look at solving an equation where the variable is on both sides.
Actually, if you’ve got the hang of solving for a variable on one side, then solving for a variable on both sides of the equation is fairly simple. It just involves one extra step. Remember when I said that the most important thing in solving for a variable was getting the variable on one side of the equation and everything else on the other side? This is why that’s so important.
Like we did on Monday, we’re going to start with an equation:
8x – 3 = 2x + 3
Let’s start by moving all of our x terms to the left. This means we’re going to subtract 2x from both sides of the equation, again keeping our equation balanced. The equation now looks like this:
6x – 3 = 3
Now, we’ll group the non-x terms to the right. For this step, we’ll add 3 to both sides, still working to keep the equation balanced. This leaves us with this:
6x = 6
Now we can divide both sides by 6 to get:
x = 1
See? It’s just like solving an equation with the variable on one side, with an additional step of moving the variable terms to be on the same side.
[...] this point, you’re comfortable with solving for a variable on one or both sides of the equation, right? Honestly, solving simple inequalities isn’t much different. [...]
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