Can someone please show me how to work through these problems?

Question

Solving for x--and they are not missed typed:
2(x-3)-3(x+5)=3(x-2)-7 and also
3x-5(3x-7)=2(x-9)+45
I would really like it if someone could show me how to solve these so I can learn how to do them, thanks.

Answer 1

first, get rid of those parenthesis. They show multiplication, so youll have:
2x-6-3x-15=3x-6-7
Now, put all terms containing x in one side and the rest on the other:
2x-3x-3x=-6-7+6+15
Now simplify:
-4x=8
Now, multiply both sides by -4:
x=-2
The other one is very similar:
3x-15x+35=2x-18+45
3x-15x-2x=-18+45-35
-14x=-8
x=4/7

Answer 2

You start with this 2(x-3)-3(x+5)=3(x-2)-7
Let's do just the left side first.

Step 1: Multiply the number on the outside of the brackets with each term inside the brackets.
Which is 2 times x and 2 times -3. Then -3 times x and -3 times 5.
So now: 2x - 6 - 3x -15 is on the left.
Now do the same on the right: 3 times x and 3 times -2 then just 7
So now you have: 2x - 6 - 3x - 15 = 3 x - 6 - 7

Step 2: The next step is to combine like terms. (Like terms in this problem are numbers with an x after them seperate from those without x's and to combine them just add the like ones together)
Just do the left side first again: 2x and -3x are like terms and -6 and -15 are like terms.
So the left side is now: -1x - 21
Do the same thing on the right: 3x is on it's own because there is no other number with an x after it. But you do need to combine -6 and -7 to get: 3x - 13 on the right.
Here's what you have so far: -1x - 21 = 3x - 13

Step 3: Move all the x's to one side.
I'll move them to the left. To do this you just move it to the other side and switch the sign. -x - 3x = -13 +21
See how the -21 moved to the right and became +21 and the 3x moved to the left and became -3x?

Step 4: Combine like terms again and this time that is everything on each side. so -1x - 3x becomes -4x and -13 + 21 becomes 7.
So the problem looks much friendlier now: -4x = 7

Step 5: Solve for x by making it the only thing on one side. In this case divide both sides by -4 so the answer is x= 7/-4 or -1.75

Just pay close attention to those negative signs.
Try those steps with the other problem, notice the -5 and the 2 are the numbers outside of the brackets. Good Luck!

Answer 3

2(x-3)-3(x+5)=3(x-2)-7
first you distribute to work out the parentheses
2x-6 which is the 2 *x then 2 * -3
then -3x-15 which is the -3 *x then -3 *5
= 3x-6 which is 3 *x and 3 * -2
next you just bring down the -7 so it would all together be
2x-6-3x-15=3x-6-7
at this point you would combine like terms
2x-3x gives you -x
-6-15 gives you -21
3x is left alone and -6-7 gives you -13 so the next step would be
-x-21=3x-13
now you want to get all the variables (x) on the same side and the numbers on the other
add x to each side of the equation to get -21=4x-13
then add 13 to each side to get -8=4x
next you want to isolate your variable (x) by dividing by 4
so you have -2=x

using the same process for the second it would go like this
3x-5(3x-7)=2(x-9)+45
3x-15x+35=2x-18+45
-12x+35=2x+27
35=14x+27
8=14x
4/7=x

Hope this helps you.

Answer 4

The idea is to isolate the variable on one side of the equation and the values on the other. Perform all () calculations first:
2x-6-3x-15=3x-6-7. Now, move your variable to the left and the values to the right, changing signs as necessary: 2x-3x-3x=-6-7+6+15. Next, combine values: -4x=8. Then, divide both sides to end up with a single, positive variable (x) -4x/-4=8/-4 -> x=-2. You do the other one.

Answer 5

I don't think I should give you the answer but I will give you a direction to go: If you expand the equasions (multiply them out) you can combine all the common terms and probably solve for x. Ex: 2(x-3) becomes 2(x)-2(3) becomes 2x-6
Hope this Helps! :)

Answer 6

2(x-3)-3(x+5)=3(x-2)-7
(2x-6)-(3x+15)=(3x-6)-7
2x-6+(-3x-15)=3x-13
-x-21=3x-13
-4x=8
-x=2
x=(-2)
I hope that walk through helped
3x-5(3x-7)=2(x-9)+45
3x+(-15x+35)=(2x-18)+45
-12x+35=2x+27
-14x=8
-x=(8/14)
x=(-4/7)

Answer 7

Multiply them out.
Add the x terms and the numbers.
Manipulate so the x is on the left and the number is on the right.

Answer 8

My Dear Aunt Sally= multiply, divide, add, subtract; i.e., do everything in brackets first that can be done, then do everything in MDAS order.