Solving equations using the index finger method

​ ​Here are the balance scales again. There are now four secret boxes in one bowl together with two one-kilogram weights. And in the other bowl, there are two five-kilogram weights. How much does one secret box weigh? We draw the scales as an equation - 4x+2=5+5.

First, we tidy up a bit and simplify 5+5 to 10. Before, we used to put our index finger over the unknown number - x. But now, we have 4x+2. You now put your index finger over the whole term that includes x. Now we can ask, what number should you add to 2 to get 10?

Eight, of course. So what you have under your finger is worth 8. Lift your finger to see what is worth 8. We then write it like this - 4x=8. 4x, which means 4 times x.

When there is no mathematical operation between a number and an unknown variable, this always means multiplication. Now, lift your index finger again and cover only the x. A new question then arises. What number should you multiply by 4 to get 8? Yes, 2.

So what you have under your finger is worth 2, and under your finger is x. X equals 2. ​ ​This way we used the index finger method in two steps. First, we covered the entire term that included the unknown variable x and calculated its worth. Next, we covered just the unknown variable and calculated its worth. We peek into the boxes to check if we are right, and yes, there are two one kilogram weights in each.

Normally, you do not have scales to check if you have done it right, but there is a trick how to test if you solved the equation correctly. We calculated that x=2. We can then plug that value in the original equation and to check if it is correct. Like this, the original equation was 4x+2=10, and we calculated that x=2. So we've replaced the variable x with a 2 like this.

Then we just calculated. Four times 2 is 8 and 8+2 is 10 and 10=10, so yes. When x=2, this equation is correct. ​ ​Let's take another example, a bit quicker. Keep up. 7=2y+y-2.

We use y instead of x this time, but it works exactly the same way. First, we simplify by gathering all terms with the same variable together. The y+y is 3y. We then covered the term that includes the unknown variable. What number minus 2 is 7?

Nine minus 2 is 7. What is under the finger equals 9, and under the finger is 3y. So 3y=9. Next step, cover only y. Three times what equals 9?

Three times 3 is 9. What is under your finger equals 3. Y=3, and then we test it. Put y=3 in the original equation. Replace all ys with 3 and calculate to the value.

Yes, the equation is correct, we did it right. Y=3. Three things to remember. The term variable means an unknown number that can change its value. Use the index finger method in two steps.

First, cover the whole term where the unknown variable is and find the value of that term. Then, cover just the variable and find its value. Even though x is a common name for a variable, a variable can be called something else just as well.