12p+4=32-2p. my son is struggling with his maths homework and I'm no help. He needs to show workings .thanks

Answer 1

I think instead of answering this particular equation, it would be better to explain how it works, then your son can apply to any similar equation.

Basically, in order to work out the value of any symbol, all the symbols (in this case "p's") need to be on one side of the equal sign, and all numbers on the other.

The positive and negative signs belong to the numbers/symbols following them. Whenever you move either numbers or symbols across an equal sign, you need to change its positive/negative value. In this example then, you would need to move the the -2p from the right side of the equal sign to the left. Then you would need to move the +4 from the left side of the equal sign to the right.

Once you have done this, you will end up with 12p + 2p = 32 - 4
Simplify each side of the equation by doing the actual maths on each side. In this case, it will leave you with 14p = 28.

Now, the number in front of the symbol is an indication of how many of those symbols there are. In this case, it is 14. This is a representation of multiplying, so there are 14 x p.

The ultimate goal of equations is to change them so that the symbol is left on its own - this is the only way you will be able to find its value.

In the same way as adding becomes subtraction across the equal sign (and vice versa), multiplication becomes division (and vice versa). Therefore, in this case, the 14 (a representation of multiplication) on the left side of the equal sign needs to move to the right, which means that 28 needs to be divided by 14. This leaves p = 2.

It is vital to always check your work, and the best way to do this is to substitute your answer for the symbols in the original equation. If your answer is correct, then each side of the equation will have the same value (hence "EQUATION")
Hope this helps not only in this case, but in others...

Answer 2

To help your son, get him to express what the question is more clearly. All of the answers have assumed he needs to solve the equation, that is find the value of p. I know that is obvious but as he progresses it will not always be so.

Also, as he learns it will be helpful if he can described each step in words so that he re4ally shows that he understands what he is doing. He doesn't have to write these words but sometimes it becomes obvious that someone has just copied an answer.

12p + 4 = 32 - 2p

Take 4 from both sides:

12p + 4 - 4 = 32 - 2p -4

12p = 28 - 2p

Add 2p to both sides:

12p + 2 p =28 -2p + 2p

14p = 28

Divide both sides by 14:

14p/14 = 28/14

p = 2

It is always a good idea the develop the habit of checking an answer where that is possible. Here, you replace p in the original equation with the answer 2. Hence:

12p + 4 = 32 - 2p

Substituting p = 2 gives

(12 x 2) + 4 = 32 - (2 x 2)
24 + 4 = 32 - 4
28 = 28 which is correct

Answer 3

if 12p + 4 = 32 - 2p
12p + 2p = 32 - 4
14p = 28
p = 28/14
p = 2

Answer 4

=> 12p + 4 = 32 - 2p
=> 12p + 2p = 32 - 4
=> 14p = 28
=> P = 28 / 14
=> P = 2

Answer 5

Rearrangement.

If 12p + 4 = 32 - 2p then
12p = 32 - 4 - 2p so
12p + 2p = 32 - 4

which makes 14p = 28
so p = 28/14
p = 2


OK?

Answer 6

The equation your son is trying to solve is a simultaneous equation, I will try my best to give a step by step explantion for this equation, but I would advise you that the best way to teach him is to speak to his teacher or arrange private tution.

I speak through experience as I did Maths and Further Maths at A Level and went on to study it at university.

All simultaneous equations have a few simple rules to them:
(a) What you do to one side you do to the other - a bit like old school weighing scales, need the same weight on both sides to keep them level.
(b) Put all like terms together.

Using this I will try to help you so you may explain it properly to your son.

12p + 4 = 32 - 2p

If we add 2p to the Right Hand Side (RHS for short) then we will not be left with any p's, but REMEMBER the same must be done to the Left Hand Side (LHS for short)

12p + 4 + 2p = 32 - 2p +2p

Rearrange to get

12p + 2p + 4 = 32

Solve to get

14p + 4 = 32

Need like terms on the same side again

14p + 4 - 4 = 32 - 4

solves

14p = 28

Solution p = 14

Depending on his age, trying using real life examples to make him understand better. Also practice makes perfect.

Answer 7

First, plus 2p on each side that has p.
Second, minus 4 from both side.
So -2p+2p=0p, and 12p+2p=14p
Then, 4 - 4=0, and 32 - 4= 28.
So the answer is 14p= 28
put 14p over 14, and 28 over 14.
So it should look like this 14p/14 = 28/14
so x= 2, because 14/14=1p and 28/14=2

Answer 8

A long since simple rule that never seems to be stressed, but is the fundemental rule that must be understood and makes it all so easy.

You can add, subtract, multiply and divide one side of the equation with ANY number (1, 3, ...) or mixture (x, a, b, 2x, 5x...etc), as long as you do EXACTLY the same thing to the other side.

This keeps the equation in balance, which you must do because you were given a balanced equation in the first place.

So get all the p's on one side and the numbers on the other side.

So, ADD 2p to both sides and SUBTRACT 4 from both sides:

12p+2p+4-4=32-4-2p+2p (obviously you can now see that th p's cancel out on the right hand side to leave 0 which you can then ignore)

Once your son can see this principle - hopefully the light will come on and he may actually start to enjoy it.

Answer 9

12p+4=32-2p
+2 +2
14p+4=32
-4 -4
14p=28
/14 /14
p=2

Answer 10

12p + 4 = 32 - 2p
12p + 2p = 32 - 4
14p = 28
p = 28/14
p = 2