Is this right so far and where do I go from here?

Question

2(x - 3) - 3(x + 5) = 3(x - 2) – 7
2x – 6 – 3x + 15 = 3x – 6 – 7

Answer 1

There is one correction.

2(x - 3) - 3(x + 5) = 3(x - 2) - 7
2x - 6 - 3x - 15 = 3x - 6 - 7

Notice that when you distribute that 3 for the second set of brackets, what you're really distributing is -3 (because of the minus sign to the left of it).

Answer 2

2(x - 3) - 3(x + 5) = 3(x - 2) – 7
2x – 6 – 3x + 15 = 3x – 6 – 7 good start. combine like terms
-x+9=3x-13 add x to each side
9=4x-13 add 13 to each side
22=4x divide both sides by 4
x=22/4=11/2=5.5

Answer 3

Actually it would be...

First: use distribution > multiply the outside term with the terms in the parenthesis on both sides...

2(x) - 2(3) - 3(x) - 3(5) = 3(x) - 3(2) - 7
2x - 6 - 3x - 15 = 3x - 6 - 7

Sec: combine "like" terms...

2x - 3x - 6 - 15 = 3x - 13
- x - 21 = 3x - 13

Third: subtract 3x from both sides...

- x - 3x - 21 = 3x - 3x - 13
- 4x - 21 = -13

*Add 21 to both sides...

- 4x - 21 + 21 = -13 + 21
- 4x = 8

Fourth: Solve for "x" by isolating it on one side > divide both sides by - 4...

- 4x/-4 = 8/-4
x = - 2

Answer 4

2(x - 3) - 3(x +5) = 3(x - 2) - 7
2x - 6 - 3x - 15 = 3x - 6 - 7
2x - 3x - 3x = - 6 - 7 + 6 + 15
-4x = 8
x = -2

Answer 5

you got the right procedure, just remember these two things:

first -- When expanding the brackets remember negative times positive = negative... all else = positive*. ie : (+)(-) = (-)...
(+)(+)=(+) ...(-)(-)=(+)
{this also applies for division}

so in line 2 for the second bracket you have -3 times (+x + 5)

remember "x" is actualy (positive 1 'x') thats why you got (negative 3x... ie '-3x') but for the 5 it is " -ve3 times +ve5
<-ve means negative +ve means positive>
hence you shouldve got "negitive" 15

second-- take any equation to be an "addition" of 'terms'
so 2+3 is really +ve2 plus +ve3 = (as we all know 5.. +ve 5)
and 2 -3 is ==> +ve2 plus -ve3 = -ve1 (use your number line if you dont see that, practice practice ect, blah ,blah)
now, a "term" is anything that is beign multiplied or divided
so 2x is one term... 56xyg is one term
2x/4 + 56abc is two terms there ect ect ect
a bracket is a term

so less talk, heres what it looks like..
2(x-3) - 3(x+5) = 3(x-2) - 7 .... four terms in this equation (-ve7 is a term by itself)

expanding first bracket only...
(+ve2)(+ve1x) + (+ve2)(-ve3) ...
=+ve2x + -ve6
so first bracket is the same as "2x-6"

now add the second term ie:expand & add -3(x+5)..

expanding second bracket ...
(-ve3)(+ve1x)+(-ve3)(+ve5) ... which is -ve3x + -ve15...
so the second bracket is the same as 3x-15 {not 3x+15 as you have}
{also writing x +-y, or x-+z dont look too pretty in iether case its the same as minus...ie x-y, or x+z,.. i guess you have to think about it and practice with the number line if u want} anyway.. so we have left side of the equation
"2x-6" + "-3x-15" = 3(x-2) - 7

re writing and expanding right side....

2x - 6 - 3x - 15 = 3x - 6 - 7 ... which is almost what you have
{note that now we have seven terms}

now as for whats next.. next we group the similar terms
x's whith x's ...y's with y's... g's with g's... or whatever... and pure numbers with pure numbers. this is called 'collecting' the terms

Just remember that when we do this we "add" them {even if its adding a -ve number.. eg: ect ect blah blah... its all about addition}

so collecting the terms...
2x - 6 - 3x - 15 = 3x - 6 - 7

-1x - 21 = 3x -13 ... note that -1x is the same as -x.. but I only write the 1 for clarity

so now, we have
-x - 21 = 3x -13

and what we all want to see is
x = blah blah blah
so here's how...

in an equation the "=" sign is there for a very important reason.. {of course}.. its saying whats on the left is "the same" or "equal to" or "of equal value" to whatever the heck is on the right
ie: 3 = 3 ... 3= 2+1 ... 3 = 1000 - 997 ... ect ect
in fact thats why the whole show is called an "equation"

so in our problem we have
-x - 21 = 3x -13

we want to get x alone on one side and all the other stuff on the other side. thers only one rule: the situation has to remain an "equation".

to do this we can do anything in the world to one side providing we do the 'same' to the other side eg: 3=3... 3 +5/4 = 3+5/4 ect ect

lets have the x on the right side,.. so we have
-x - 21 = 3x -13 ... now 'add' {+ve}13 to both sides
this gives
-x - 21 + 13 = 3x - 13 +13 .. now take a look at the right hand side
,you see that? : -13 +13 when we collect these it equals zero

so we have
-x - 8 = 3x + 0
that is ...
- x - 8 = 3x {note, i got the -ve8 by adding +ve13 to -ve21 }

then add {+ve}1x to both sides
this gives
0 -8 = 4x
ie
-8 = 4x

now finally divide all terms one each side by {+ve4}
in this case the left and right side have one term each.
so dividing gives..
-2 = x
rewriting give
x = -2 and thats it

of course you dont write all this mumbo jumbo on your paper, I only write it to explain.

so here's the working in one quick runthrough, exactly as I would write it on a paper(even with explanations)..


2(x - 3) - 3(x + 5) = 3(x - 2) – 7

expanding the brackets gives
2x – 6 – 3x - 15 = 3x – 6 – 7

collecting the terms
-x - 21 = 3x -13

adding 13 to both sides gives
- x - 8 = 3x

adding x to both side
-8 = 4x

dividing though out by 4
-2 = x

therefore x = -2 ans

the end
you see, thats like 5 lines or however you want to write it.
you can write the explanation for each line next to the equation instead of under. its up to you.

well any how have fun with maths.

Answer 6

Given expresstion=2x-6-3x-15=3x-6-7
=>2x-3x-3x=-6-7+6+15
=> -4x=8
=>x= 8/-4= -2 ans
k

Answer 7

Watch those signs, a negative Times a negative equals a positive,you made an error of this type
[ -3(x+5) = (-3x-15) ]