math
7th Grade - Equations

7th grade lesson

6 - Equations


An equation is something like : 2x + 4 = 12 or -2x - 4 = 7x - 15. You must find x. This is how we solve equations :

2x + 4 = 12
2x = 12 - 4
2x = 8
x = 8 2
x = 4
3x + 9 = 15
3x = 15 - 9
3x = 6
x = 6 3
x = 2
5x - 10 = 15
5x = 15 + 10
5x = 25
x = 25 5
x = 5

In fact, do you know your multiplication tables well? In order to know for sure, draw a circle, write a number at the centre and on the circle write 10 numbers from 0 to 9 in any order. Example :
circle for the learning of multiplication tables

If you are able to go round the circle by giving the result of the 10 multiplications in less than 20 seconds, it means that you know the 7 times table very well. If you do not know the multiplication tables well, there is no use continuing with this lesson, you need to learn them ! (Learning the tables, 2nd grade lesson)


If you already know your tables, let's get back to the equations. The aim is to find x.

2x + 4 = 12

If we take away 4 from both sides, the equation is still valid. Therefore 2x + 4 - 4 = 12 - 4. Finally this gives us 2x = 12 - 4. In practice, we never write the intermediate step, we immediately write 2x = 12 - 4. In fact when we move a term to the other side of the = sign, we change the sign of that term. Examples :
4x - 12 = 2x + 4
4x - 2x = 4 + 12
2x = 16
x = 16 2
x = 8
5x - 10 = 15x - 5
5x - 15 x = -5 + 10
-10x = 5
x = 5 (-10)
x = -0,5
12x - 4 = 16x - 10
12x - 16x= -10 + 4
-4x = -6
x = -6 (-4)
x = 1,5
You would have noticed that during the last step of the equation, we divide both sides by the number that is in front of x, even if it is negative. Indeed, if you have 3x and you wish to find x, you have 3 times more so you have to divide by 3, and in order for the equation to be always valid, when you divide on the left, you must also divide on the right (if you don't understand all that, it is not a big problem but you must know how to do it).


See also : algebra on fmaths.com



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