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

Question

Solve and prove

Answer 1

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

First: eliminate parenthesis --- distribute the outer terms with the terms in parenthesis....

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

*Combine the terms...

2x - 6 - 3x - 15 = 3x - 6 - 7
2x - 3x - 6 - 15 = 3x - 6 - 7
- x - 21 = 3x - 13

Sec: add "21" by both sides...

- x - 21 + 21 = 3x - 13 + 21
- x = 3x + 8

*Subtract "3x" from both sides...

- x - 3x = 3x - 3x + 8
- 4x = 8

Third: isolate "x" on one side --- divide both terms by "-4"...

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

*Check/Prove the Solution: Replace "-2" with the x-variables in the equation...

2(-2-3) - 3(-2+5) = 3(-2-2) - 7
2(-5) - 3(3) = 3(- 4) - 7
- 10 - 9 = - 12 - 7
- 19 = - 19
True

Answer 2

5(3x + 2) - 3(2x - 7) 15x + 10 -6x +21 9x - 11 15-2(x + 1) = 3x + 7 15 -2x -2 = 3x + 7 13 - 5x = 7 -5 x = -6 x = 6/5 The median of a group of numbers is that number in which half of the values are greater than the median and half are less than the median. In this case you have an even amount of numbers so the median here is (60 + 50) /2 or 55. 2y = x = 8 2y = x y = x/2 or y = 4 (3x-2) 2 = 6x - 4

Answer 3

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

- x - 21 + x = 3x - 13 + x

- 21 = 4x - 13

- 21 + 13 = 4x - 13 + 13

- 8 = 4x

- 8/4 = 4x/4

- 8/4 = x

- 2 = x

The answer x = - 2

Insert the x value into the equation

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

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

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

2(- 5) - 3(3) = 3(-4) - 7

- 10 - 9 = - 12 - 7

- 19 = - 19

- - - - - - - - - - - - - -s-

Answer 4

you are missing a right parentheses on the LHS of this equation, so i'll include it for you....
Equation becomes 2x-6-3x-15=3x-6-7
=>gathering both set of coefficients together on either side of the equals sign gives -8=4x=> x=-2
Proving it by putting back into the equation gives 2(-5)-3(3)=3(-4)-7
=>-19=-19 QED

Answer 5

2x - 6 - 3x - 15 = 3x - 6 - 7
2x - 3x - 3x = - 6 - 7 + 15 + 6
- 4x = 8
x = - 2

Check
LHS = 2(-2-3) - 3(-2 + 5) = -10 - 9 = -19
RHS = 3(-2 - 2) - 7 = -12 - 7 = -19

Answer 6

x=4

Answer 7

x=-2

Checking the work:
2(x-3)-3(x+5=3(x-2)-7
2(-2-3)-3(-2+5)=3(-2-2)-7
2(-5)-3(3)=3(-4)-7
-10-9=-12-7
-19=-19

Answer 8

first you foil it: (2x-6)-(3x+15)=(3x-6)-7
then combine like terms: -x-9=3x-13
get variables on one side: 4=4x
get x by itself: 1=x

And to prove it just plug the value for x which is 1 into the original equation

Answer 9

2x-6-3x-15=3x-6-7
-x-21=3x-13
-x-3x-21=3x-3x-13
-4x-21=-13
-4x-21+21=-13+21
-4x=8
-4x/-4=8/-4
x=-2

Answer 10

-19 is answer.