Introduction to linear equations

Introduction to linear equations 

Forming and solving linear equations is usually a teething trouble that teachers and parents go through with the primary and middle schoollers. Here I am going to share my experience in conceptualising linear equations with my kids:

STEP 1: We all are familiarised with common balance, right? We have seen that in the Grocers as well as in our home kitchens while moms measure portions of flour for cake making. Now let us weigh an apple using the balance and let us also assume that an apple weighs exactly 10 gms. So, our balance will look like this after putting a 10 gms weight to counter the apple.

This gives us the first equation! Clearly, we use the “=” sign because the weight of the apple is exactly 10 gms.

STEP 2: Let us add 5 gms weight to one side of the balance. And then

It is no longer balanced! 15 grams on the right hand side of the balance is certainly heavier than the apple that was mere 10 grams.

STEP 3: Let us balance this then. Just an addition of a 5 gms to the left side (apple side) will do the trick.

So, we have learnt that:

We need to add the same value to BOTH side of the equation without disturbing the balance.

STEP 4: Let us do the same experiment of adding the same “thing” to both sides. Say, we add an orange to the left and right hand side. The “equation” continues to balance.

STEP 5: Let us add 5 gms again to either side. It will obviously remain balanced.

STEP 6: Can we now subtract 5 gms from either side? Looks like, we can.

So, we have learnt that:

We need to subtract the same value to BOTH side of the equation without disturbing the balance.

STEP 7: Let us go back to our apple + orange equation once again. Let us just DOUBLE the quantities on either side. The balance remains horizontal, i.e the equation remains balanced.

So, we have learnt that:

We need to multiply BOTH sides of the equation with the SAME VALUE so as not to disturb the balance.

Solving the first equation

Introduction to solving linear equations

The problem: Let us look at our apple and balance example to form an equation like the below:

Clearly, there are "known" and "unknown" values in the equation. The weights with 1 (gram) values are known because we exactly know how heavy each of them is. The weight of the apple is unknown and denoted by "A" here.

It is customary to keep the unknowns in the left hand side of the equation. No reason here. It is just some practice that we follow and we need to get used to.

So, let us try to find the weight of an apple. We can safely remove the three (3) weights from either side without disturbing the balance, right? That is also as per the lesson learnt in the previous post that we can subtract the same amount from either side of the balance so as not to disturb the balanced state. Lets see how that looks:

Now, we have learnt recently (previous post) that we can divide the left and right hand side by the same number so as not to disturb the balance.

Finally, we solved the equation. The value of A is 6! So, this is how we arrived at it: