DragginMath: Solving Equations
After all this time, you are probably wondering how to solve an equation in DragginMath.
Enter 3x+4=10.
Drag 4 up onto =. The result is 3x=10–4.
Double-tap − to evaluate 10–4. The result is 3x=6.
Drag 3 up onto =. The result is x=6÷3.
Double-tap ÷ to evaluate 6÷3. The result is x=2.
The Properties of Equality used to solve equations are all invoked by dropping operands on =. What DragginMath then does internally is equivalent to the classic mantra of algebra: “Do the same thing to both sides.” You see the result after work has been done on both sides and then cleaned up. That’s all you need to know to solve equations in DragginMath. Really.
Do it again, but with fewer moves this time. Use ↩️ to undo this example back to 3x+4=10, Drag 3 up onto =, then double-tap ÷. The result is still x=2. As with evaluation, you can solve one operation at a time, or several at a time, or even all at once, depending on how much detail you want to see.
Perhaps you are not sure what to drag onto =. This analogy might help:
Imagine there is a loose pile of sticks in your yard. It is quite a pile, maybe several feet high. And for some reason, you drop your phone onto the pile of sticks. It falls farther and farther into the pile, until finally you see it through the gaps in all those sticks, lying on the ground. Of course, you want to get it back. There are two ways you might try to do this:
1) Reach down into the pile, hoping your arm is long enough to grab your phone down there on the ground.
2) Pull the sticks away, one or several at a time, until your phone is left by itself with no more sticks around or over it.
DragginMath only knows about the second method: pull operands away from what you want to find. Whatever operand you pull away, drag it up in Blue Mode and drop it on =. The relevant operators will be inverted onto the other side.
There is one complication. In a minimal example, x=2, drag 2 up onto =. DragginMath shows a dialog asking if you want to use subtraction or division to make this change, or maybe if you want to cancel the change. If you choose subtraction, the result is x–2=0. If you choose division, the result is x÷2=1. Sometimes, this is useful. Usually, it means you tried to pick up the whole pile of sticks and walk away with it when you didn’t really intend to do that. If this is what happened, choose to cancel the change and think about what you really meant to do. In this minimal example, there isn’t anything else you can do.
Cleaning Up (or Not) After Solving
Enter x+2=5, then drag 2 up onto =. In the default configuration, the result is x=5-2.
But what about “Do the same thing to both sides”? It appears that DragginMath did two different things, one to each side. Would you like to see everything that happened? You can.
Tap the Configuration button ≡ in the upper right corner of the screen, then turn off Clean Solve and tap OK. Now solve this equation again.
Enter x+2=5, then drag 2 up onto = to get x+2–2=5–2. Now you can see that DragginMath really did subtract 2 from both sides. On the left side, drag + up onto –. This associates the 2s together as x+(2–2)=5–2. Drag either of the 2s sideways past the other to cancel into x+0=5–2. Drag 0 up onto + to simplify as x=5–2.
You will quickly tire of doing these repetitive cleanup steps. But you must understand that they need to happen, and you must know how to do them.
When DragginMath is first installed, it assumes you want Clean Solve, where equations are automatically cleaned up after each move. But if you are truly new to algebra, you may want to turn off Clean Solve for a while so you can see and be involved with everything that has to happen for algebra to work correctly. Be sure to manually clean up immediately after each action involving =. If you don’t, your equations will quickly become too complicated to understand. After you are comfortable with this aspect of algebra, turn on Clean Solve again, but be aware of these steps that DragginMath is doing for you.