Equations and Inequalities
Solving Equations for Expressions
We can also solve equations for expressions that aren't single variables. We can solve an equation for x2, or 2x, for example. We can sense your eager anticipation. We won't make you wait any longer.
Solve the equation A = π r2 for r2.
Divide both sides by π to find that .
Because we have r2 all by itself on one side of the equation, and no copies of r on the other side, that is it. Gosh, it seems like so little work for such an ugly-looking expression. Good thing we're all about inner beauty here.
Solve the equation y = 2x - 9 for 2x.
Add 9 to both sides to find that y + 9 = 2x. We're already done. Whoa, we barely started! If we were solving for x, we would divide both sides by 2, but since we are solving for 2x, we don't even need to bother. We can use all that extra time we saved to volunteer at a homeless shelter. Or...to play another level of Call of Duty.
When we are solving for an expression involving x—say, x2—we want to end up with a formula for x2 that doesn't have any x terms in it. Having a formula such as
isn't helpful, because if we knew x then we would know x2 without needing to use some fancy formula. Even though we would probably try to figure out the fancy formula before realizing that. Doh.
Be Careful. Remember to answer the question that is asked. If you are told to solve for 2x, don't do extra work to solve for x if you don't need to. Your time is precious. Time is money. That's money in the bank. You can take that to the bank. We think you see where we're going with this train.