solving equations

[christy053]

how do you solve the following equations and a simple way to work them out please they relly annoy me

1.a+4=4a-2

2.6(x-4)=18

3.x+7 over 3 = 8


please help christy x-x-x-xx-xxxxx

[shammydodger]

1. Subtract a from both sides of the equation:

4 = 3a-2

Then add 2 to each side:

6 = 3a

Then divide both sides by 3:

2 = a

2. Expand the brackets:

6x - 24 = 18

Add 24 to both sides:

6x = 42

Then divide both sides by 6:

x = 7

3. Multiply both sides by 3:

x + 7 = 24

Subtract 7 from both sides:

x = 17

[christy053]

awwwwwwwwwwwwwww ta i get you now so you have to like cancel down both sides

[teacher1]

1. you have to group like " things" - numbers , letters.

a + 4 = 4a - 2

+ 4 + 2 = 4a - a +6 = 3a 3a = 6 a = 6/3 a = 2 As the numbers/letters change sides of the equation they change positive to negative / negative to positive - the a goes across and becomes negative and the -2 becomes +2

[teacher1]

Now I've put my answer it looks really complicated - sorry!

[christy053]

wow ! sorry teacher1 i dont undertsand that :-( sorry

[shammydodger]

Christy

Exactly. Whatever you do to one side of the equation, you must also do to the other.

[dancecaller]

When we learnt it we were made to write them out the long way for ages so; a=2a-3 becomes 3+a=2a-3+3 becomes 3+a-a=2a-a becomes 3=a. After a bit it was obvious that "take 3 away from both sides" gave the same answer as "move the 3 to the other side and change + to -" but the first explained why it worked, the other way is a shortcut.

If you do the same thing to one side as the other and they were equal before, they will still be equal.

Shortcuts are move it to the other side and change
+ to �
- to +
multiply to divide
divide to multiply

You can figure out why the others work, for yourself. We were not allowed to use the shortcuts at first to avoid garbling them through not understanding.

[dancecaller]

Teacher's suggestion about grouping things was the aim of all this adding etc. - to get the letters on one side, numbers on the other

[dancecaller]

Sorry, I should have said :- After a bit it was obvious that "add 3 away to both sides" gave the same answer as "move the 3 to the other side and change - to +"

Both are true, but the one I wrote didn't fit the example I gave