The '-3' is on the left hand side, when you move it to the right hand side, why did it turn into '+3' ?

This is an important operation which you will need to understand in algebra in the coming years.

Suppose 9 - 3 = 6.

I want to make the 9 alone on the left hand side, so I need to move the 3 over to the other side.

Then, it follows that 9 = 6 + 3, and not 6 - 3.

What actually happens is that we add 3 on both sides of the equation, so that

(9 - 3) + 3 = 6 + 3
9 - 3 + 3 = 6 + 3

and the “-3 + 3” on the left side of the equation gets eliminated, leaving us with

9 = 6 + 3

In short, whenever we wish to move a “-3” over to the right hand side, we need to change the sign from “-“ to “+”. Similarly, we to move a “+3” over to the right hand side, we need to change the sign from “+” to “-“.

Let’s see how it works in algebra.

x - 8 = 3

To bring the “-8” over, we convert it to “+8” on the other side.

x = 3 + 8
x = 11

Check that in the original equation, 11 - 8 does equal to 3.

If you are not comfortable with this approach, you can still do the traditional way of adding the same number to (or subtracting the same number from) both sides of the equation.

x - 8 = 3
x - 8 + 8 = 3 + 8
x = 3 + 8
x = 11

It’s actually what you have been doing in primary school!

_____ - 8 = 3

What is the missing number?

Think of this example and you will then realise why the “-8” becomes “+8” as you try to solve for _____ which is of course 11.

Division and multiplication work in a similar way too.

thanks :)

The division and multiplication idea is the same.

Suppose 2x = 8.

We wish to find the value of x which fits into the above equation, in other words, x is that number which is multiplied by 2 to become 8.

From what you have learnt in primary school, if (blank) * 2 = 8, then

(blank) = 8 / 2 (where / is the division symbol)
(blank) = 4

As we can see, whenever we have a multiplier attached to the x (in this case, 2), we bring over the “2” to the other side as a divide, since it was originally attached on the left hand side as a times.

More examples.

x + 3 = 9
x = 9 - 3
x = 6

This is very similar to

____ + 3 = 9
____ = 9 - 3
____ = 6

if you observe carefully.

Another one.

x - 5 = 3
x = 3 + 5
x = 8

This is very similar to

____ - 5 = 3
____ = 3 + 5
____ = 8

if you observe carefully.

3x = 15
3 * x = 15
x = 15 / 3
x = 5

This is very similar to

3 * ____ = 15
____ = 15 / 3
____ = 5

And for the division version.

x / 5 = 4
x = 4 * 5
x = 20

This is very similar to

____ / 5 = 4
____ = 4 * 5
____ = 20

Let’s put these ideas together.

(2x - 5) / 3 = 7

The first annoying thing is the fraction, which is caused by the denominator 3. Fractions and divisions are technically the same thing.

To counter the “divide by 3”, we “multiply by 3” on the other side.

2x - 5 = 3 * 7
2x - 5 = 21

The next thing is that “-5” attached to 2x - 5. To get rid of this “-5”, we bring it over to the other side as a “+5”

2x = 21 + 5
2x = 26

Finally, we get rid of the “2 in front of x by bringing it over as a divide.

x = 26 / 2
x = 13

And this is what we need to know for algebra at the Sec 1 level.

ah I see. Thank you I understand better now

I have one question in mind. Does this only work if we move '-3' to the right hand side?
Does it apply the same if we are moving from right hand side to left hand side?

As long as the term is brought over to the other side of the equals sign (whether left to right or right to left), the positive/negative sign must be changed.