Question

Solve and show work:

1. Solve x-8a/6=3a-2x for x
2. Solve 3x-2a=7a for a
3. Solve 3(bx-2ab)=b(x-7a)+3ab for x
4. Solve 2x+3b/9=x-b/2

Answer 1

Im a keep editing since this is timed.

#1 x-8a/6=3a-2x

Multiply each term by 6 to remove fraction .

6(x-8a/6)= 3a(6)-2x(6)

X-8a=18a-12x

Add 12x both sides

X+12x-8a=18a-12x+12x

13x-8a= 18a

Add8a both sides

13x-8a+8a=18a+8a

13x=26a

Divide each side by 13

13x/13=26a/13

X= 26a/13

Reduce and cancel common factor .

X= 13(2a)/13(1)

X=2a/1

X=2a

Problem #2

3x-2a=7a find a

Subtract 3x both sides

3x-3x-2a=7a-3x

-2a=7a-3x

Subtract 7a both sides

-2a-7a=7a-7a-3x

5a=-3x

Divide both sides by 5

5a/5=-3x/5

A= -0.6 or -3/5

Problem#3

3(bx-2ab)=b(x-7a)+3ab

Distributed property

3(bx)+3(-2ab)=b(x)+b(-7a)+3ab

Simplify

3bx-6ab=bx-7ab+3ab

Add -7a plus 3ab on right side

3bx-6ab= bx-4ab

Subtract bx both sides

3bx-bx-6ab= bx -bx -4ab

Simplify

2bx-6ab= -4ab

Add 6ab both sides

2bx-6ab+6ab=6ab-4ab

2bx=2ab

Divide 2b both sides

X= 2ab/2b

Cancel 2 common

X= ab/b

X=a

Answer 2

For solving an equation for a variable, we need to isolate the variable in the left side of the equation,

1. Given equation,

`(x-8a)/(6)=3a-2x`

`x-8a = 18a - 12x` ( By cross multiplication ),

`12x+x-8a-18a=0`

`13x-26a=0`

`13x = 26a`

`\implies x = 2a`

2.
`3x-2a=7a`

`-2a-7a=-3x`

`-9a=-3x`

`\implies a = (x)/(3)`

3.
`3(bx-2ab)=b(x-7a)+3ab`

`3bx-6ab = bx - 7ab + 3ab`

`3bx - bx = 6ab - 7ab + 3ab`

`2bx=2ab`

`\implies x = a`

4.
`(2x+3b)/(9)=(x-b)/(2)`

`4x+6b = 9x - 9b`

`4x - 9x = -6b - 9b`

`-5x=-15b`

`x=3b` ( For x )

`b=(x)/(3)` ( For b )