help for a frustrated mum wanting to help son !?

Question

'simple (ha! not for me - mathematically challenged!) equations'. Can anyone show simple working out for following:-
-x + 3 = 6
-x - 3 = 7
9x - 6 = 8
6x = 28
a_
4 = 7
3 (2x + 5) = 75
In hope.......

Answer 1

The trick is to move the unknowns (letters) to one side and the numbers to the other side :

-x + 3 = 6

-x = 6 - 3 ; note how the sign of the 3 changes

-x = -3

thus x = 3 ;

--
9x - 6 = 8

9x = 8 + 6 ; // again sign of the 6 changes
9x=14

x = 14/9; ( divide both sides of the equation by 9

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Answer 2

I know where you're coming from!! I have to struggle through with my kids' maths as well! I'll give it a go for you:

1.) -x + 3 = 6
-x = 6 - 3
-x = 3
x = -3

2.) -x -3 = 7
-x = 7 + 3
-x = 10
x = -10

3.) 9x -6 = 8
9x = 8+6
9x = 14
x = 14/9
x = 1.56 or one and 5 ninths.

4..) 6x = 28
x = 28/6
x = 4.67 or 4 and 4 sixths.

5.) Not sure if the next two lines are meant to be together - is it
a - 4 = 7? If so,
a = 7 + 4
a = 11

6.) 3(2x+5) = 75
(6x + 15) = 75
6x = 75-15
6x = 60
x = 10

Answer 3

The idea is to isolate X, to have only one X on one side of the equal sign. You do that by adding or substracting the same values on both sides of the equal sign, or by multipliing or dividing by the same value on both sides, and by simplyfiing cancelleing terms

Here is how you do it:

-x + 3 = 6
-x + 3 - 3 = 6 -3
-x + 0 = 3
-x = 3
x = -3

Other example:
9x - 6 = 8
9x - 6 + 6 = 8 + 6
9x = 14
9x/9 = 14/9
x = 14/9


The last example requires distributing the multiplication over the addition:
3 (2x + 5)=75
(3 * 2x) + (3 *5) = 75
6 x + 15 = 75
6x +15 - 15 = 75 - 15
6x = 60
x = 10


Got it?

Answer 4

Hi!

Sometimes algebra can be confusing simply because of all the x's, but don't worry, once you understand the rules and how the manipulate the expressions, it becomes very easy:

1) -x+3=6.
The idea is to try and find the value for x; that is, you need to get x on its own on one side of the equation. To do this, you need to add, subtract, multiply, divide etc, but remember that what you do to one side of the = sign, you have to do to the other. So,
-x+3=6
-x=3 (subtract 3 from both sides)
x= -3 (multiply both sides by -1)

2) This is similar to the first one:
-x-3=7
-x=10 (add 3 to both sides)
x= -10 (multiply both sides by -1)

3) 9x-6=8
9x=14 (add 6 to both sides)
x=14/9

4) 6x=28
x=28/6 (divide both sides by 6)
x=14/3 (cancelling down)

5) Is this a-4=7, or a/4=7?
For the first, just do a similar process to that which I've explained above:
a=7+4=11, hence a=11.
If you meant a/4=7, then just multiply both sides by 4 to get a=28.

6) 3(2x+5)=75.
This one looks trickier, but it isn't really! First, divide both sides by 3, to obtain:
2x+5=25
Then take away 5 from both sides:
2x=20
Then divide by 2:
x=10.

I hope this helps!

Answer 5

Answer 1:
-x + 3 = 6
-x = 6-3
-x = 3
x = -3

Answer 2:
-x-3 = 7
-x = 7 + 3
-x = 10
x = -10

Answer 3:
9x -6 = 8
9x = 8 + 6
9x = 14
x = 14/9

Answer 4:
6x = 28
x = 28/6
x = 14/3(simplified)

Answer 5:
I suppose the question is : a/4 = 7
a/4 = 7
a = 7*4
a = 28

Answer 6:
3(2x + 5) = 75
6x + 15 = 75
6x = 75-15
6x = 60
x = 60/6
x = 10

I hope those will help your boy

Answer 6

-x + 3 = 6 take three from both sides
-x = 6 - 3 miltiply both sides by -1
x = -6 + 3
x = -3

-x - 3 =7 is done the same way.

9x - 6 = 8 add 6 to both sides
9x = 8 + 6
9x = 14 devide both sides by 9
x = 14/9

3 (2x + 5) = 75 multiply out brackets
6x + 15 = 75 -15 from both sides
6x = 60 devide both sides by 6
x = 10

that should help.

Answer 7

I haven't done all of them, if x is the place holder then you need to find what value x holds. the trick is to get x on its own when ever you move a number or letter over the = you change the sign of the number or letter. so in the first example when the tree goes over it becomes negative.

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


3 (2x + 5) = 75
Multiply the 3 into the brakets
6x + 15 = 75
now you get x on its own
6x = 75 - 15
6x = 60
need to divide by 6 to get x on its own, note when you divide by one number you divid all the other terms as well (a term os a number separated by a = or a -
x = 10

good luck not so tough if you know the rules...

Answer 8

1.x= -3 2.x=-10 3. x=14/6 4.x=14/3 5. a=28 6.x=10

Answer 9

- x + 3 = 6

-x + 3 - 3 = 6 - 3

- x = 3

-1(-x) = - 1(3)

x = - 3

- - - - - - - - - - -

- x - 3 = 7

- x - 3 + 3 = 7 + 3

- x = 10

- 1( - x) = - 1(10)

x = - 10

- - - - - - - - - - - - -

9x - 6 = 8

9x - 6 + 6 = 8 + 6

9x = 14

9x/9 = 14/9

x = 1 5/9

- - - - - - - - - - - - - - - - -

6x = 28

6x/6 = 28/6

x = 4 4/6

x = 4 2/3

- - - - - - - - - -

a/4 = 7

4(a/4) = 4(7)

a = 28

- - - - - - - - - - - - - -

3(2x + 5) = 75

6x + 15 = 75

6x + 15 - 15 = 75 - 15

6x = 60

6x/6 = 60/6

x = 10

- - - - - - - -s-

Answer 10

I want to add to gimb's answer that whatever you do to one side of an equation, you must do to the other. for example if you subtract the 3 from the first equation you get
-x + 3 - 3 = 6 - 3

in the equation 6x = 28 you must divide both sides by 6 so

6x / 6 = 28/6

does that make the process clearer?