Help with equations please

[mountaingirl]

Dd has maths equations to do and she is stuck. Could anyone help her please and explain how she works this out (as well as any future ones). Thank you.

3(2x+5)= -7(3-2x)

4(2-8x)-3(-9x+1)=0

What is x?

the key thing about equations is to think of them like scales; what you do to one side you must to the other if the two sides are to remain equal (or in balance)
your dd must rearrange (move things from one side to the other) the equation so that she has x (and only x) on one side and a number on the other
STEP 1: multiply out the brackets
6x + 15 = -21+14x
STEP 2 put the numbers on one side
6x+15-(-21)=14x
6x + 36 = 14x
STEP 3
put all the xs on one side
36 = 14x-6x
36 = 8x
STEP 4
divide through by 8
36/8=18/4=9/2=x

First question
Need to get all the x terms on one side, doing the same to each side in the process.

First multiply out
3(2x + 5) = -7(3 - 2x)

6x + 15 = -21 + 14x

Add 21 to left side

6x + 36 = 14x

Take 6x from both sides

36 = 8x

x= 4.5

Top one
3(2x+5)=-7(3-2x)
mulitply out the brackets on each side
6x + 15 = -21 + 14x
then rearrange so all the x terms are on one side
15 +21 = 14x - 6x
which is
36 = 8x
so x= 4.5
which seems a bit of an odd answer so my arithmetic might be influenced by the food poisoning.

second one
4(2-8x) -3(-9x+1)=0
multiply out
8 -32x +27x -3 = 0
simplify
5 -5x = 0
put all the x on one side
5=5x
so x=1

remember a minus times a minus gives a positive number.

OK. I hope this makes sense...

First multiply out the brackets so

3(2x+5) becomes 6x+15 and
-7(3-2x) becomes -21+14x (as a minus times a minus becomes a plus)

so the first equation becomes

6x+15=-21+14x

Then put all the x on one side of the equals sign and all the whole numbers on the other side. If a figure crosses the equals it changes sign

so it now becomes

6x-14x = -21-15 (as the +14x had crossed the equal sign it became -14x on the other side and the +15 changed to -15 as it went over in the other direction).

Simplifying by adding everthing up on each side this becomes
-8x = -36

You can cancel out the minus signs as they appear on both sides so
8x=36

Divide both sides by 8
x=36/8
x=4.5

For the second one do the same. So you have

8-32x+27x-3=0 when the brackets are multiplied out

Put all the numbers on side of the equals sign and all the x values on the other so - you have to change the signs on each of the x values as they have crosses the equals sign

8-3 = 32x-27x

5 = 5x
1=x

Just to check she should use the values calculated for x and work out the sums. It should work.

I have spent so long typing this that someone much cleverer than me will have answered your question long ago.

Oh Wow! I never would have figured any of that out! :) Thank you all so much for helping me!

Thank you from me too we both really appreciate you all taking time to help.

I've been having the exact same problem, trying to remember how to work out linear equations so that i can help DS with his homework. Can anybody recommend a good website/book that I can use to explain it to him? Nothing I've looked at so far seems to give good, clear explanations.

this website has some fantastic tutorials

Thanks ggirl, just made a note of that website for when ds has an "i'm stuck" moment

Thank you ggirl, I'll give it a try