Question

1.solve the following equation for y 3x- 2y= 6

2. solve the following equation 1/3(6x-9)= 3/4(4x-8)
3. solve 3(2x-1)/4= x + 7/2
the 3(2x-1) is over the 4 and the x + 7 is over the 2 i really dont understand them

Answer 1

So,

For number one, there will be an infinite number of solutions, as there are two placeholders.
3x - 2y = 6
It seems we can use the intercept method.
3x - 2(0) = 6
3x = 6

Divide both sides by 3
x = 2

This is one solution: (2,0)

3(0) - 2y = 6
-2y = 6

Divide both sidees by -2
y = -3

This is another solution: (0,-3)
You should now be able to draw the line.
If you want intercept form for this equation, just manipulate the equation in order to get the y = mx + b form.

Subtract 3x from both sides
-2y = -3x + 6

Divide both sides by -2

`y = (3)/(2) x + 6`


For the second problem, simply manipulate the equation.

`(1)/(3) (6x - 9) = (3)/(4) (4x - 8)`

Distribute

`2x - 3 = 3x - 6`

Subtract 2x from both sides

`-3 = x - 6`

Add 6 to both sides

`3 = x`


For the third problem, do the same thing.

`(3(2x-1))/(4) = x + (7)/(2)`

We must first multiply both sides by 4.

`3(2x-1) = 4x + 14`

Distribute

`6x - 3 = 4x + 14`

Subtract 4x from both sides

`2x - 3 = 14`

Add 3 to both sides

`2x = 17`

Divide both sides by 2

`x = (17)/(2) \ or\ 8 (1)/(2)`