Solving Equations?

Question

Here are the only 2 questions I cant answer:

1. -x/3 - 12 = x

2. x/4 - 9 = -(x - 3)/ 2

For question #2: the whole thing in parenthasis is being divided by 2.

plz tell me the answer plus the work so that i understand. thanks!

btw, ur solving for X.

Answer 1

1. {18}
-x/3 - 12 = x
-x - 36 = 3x
-36 = 2x
-18 = x

2. {14}
x/4 - 9 = -(x - 3) / 2
x - 36 = -4(x - 3) / 2
x - 36 = -2(x - 3)
x- 36 = -2x + 6
3x - 36 = 6
3x = 42
x = 14

Answer 2

1. Eliminate the fraction > multiply the denominator by everything:

3(-x/3) - 3(12) = 3(x)

First: cancel "like" terms and combine the remaining terms >

- x - 36 = 3x

Sec: add "x" to both sides (opposite sides means opposite sign)

- x + x - 36 = 3x + x
-36 = 4x

Third: solve for "x" by isolating it on one side > divide both sides by 4 >

- 36/4 = 4x/4
- 9 = x
x = -9

2. Eliminate the fraction > multiply the denominator by everything: (distribute the negative sign with both terms in the parenthesis >

x/4 - 9 = -(x - 3)/2
(2)(4)(x/4) - (2)(4)(9) = [(2)(4)(-x + 3)/2]

First: cancel "like" terms and combine the remaining terms >

(2)(x) - (2)(4)(9) = (4)(-x + 3)
2x - 72 = - 4x + 12

Sec: add 72 to both sides >

2x - 72 + 72 = - 4x + 12 + 72
2x = - 4x + 84

Third: add 4x to both sides >

2x + 4x = - 4x + 4x + 84
6x = 84

*Divide both sides by 6 >

6x/6 = 84/6
x = 14

Answer 3

1. Okay, nobody likes fractions, so you're going to want to multiply both sides by three to eliminate them.

-3x/3 - 36 = 3x
-x - 36 = 3x

Okay, now you need to isolate the variable. Do this by adding -x to both sides.

-x + x - 36 = 3x + x
-36 = 4x

Finally, divide both sides by 4 to completely isolate the x.

-36/4 = 4x/4
-9 = x <---Final Answer! : )


2. Again, nobdy likes fractions, so you're gonna wanna mulitply by 4. However, this one's gonna be a little trickier, since you've got fractions on both sides and they have different denominators.

4x/4 - 36 = 4x - 12/2
x - 36 = 2x - 6

Now isolate the variable again-subtract x from both sides.

x - x - 36 = 2x - x - 6
-36 = x - 6

Isolate is some more-add 6 to both sides.

-36 + 6 = x - 6 + 6
-30 = x <----Final Answer!

Answer 4

1. -1/3 * x -12 = x
-12 = x + 1/3*x
-12 = 3/3*x + 1/3*x
-12 = 4/3*x
-12 (3/4) = 4/3*3/4*x
-36/4 = 12/12*x
-9 = x
2. 1/4*x -9 = -1/2(x -3)
1/4*x -9 = -1/2*x + -1/2*-3
-9/4 * x = -1/2*x + 3/2
-9/4* x + 1/2*x = 3/2
-9/4* x + 2/4*x = 3/2
-7/4*x = 3/2
-7/4*x = 6/4
-7x =6
x = -6/7