How would I answer this? - Solve for x (3x+1)(2x-1) = (2x-1)(4x+3)?

Question

It's in Quadratic Equations and Solutions By Factors but i have no idea what to do.

Answer 1

I beg to disagree with the previous answers are there are two solutions to this equation and not just one.

1) Simplify the equation by removing (2x-1) from both sides

So you get 3x+1 = 4x+3

This gives you , x = -2

This is just one part of the solution
2) The two equations would also be satisfied if the value 2x -1 = 0

so

2x -1 = 0
x = 1/2

So the two solutions to this equation are x = 1/2 and x = -2

EDIT
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A simple way to solve it even if you insist on multiplying both sides

After multpiplication, the equations becomes

6x^2 + 2x - 3x -1 = 8x^2 + 6x -4x -3

Simplifying it leads to
2x^2 + 3x -2 = 0

This is the tricky part. This can be rewritten as
(x + 2) (2x -1) = 0

For this to be true, either x+ 2 can be 0 or 2x-1 can be zero.

This gives us the values, x = -2 and x = 1/2
Cheers

Answer 2

Multiply each side by the same number in this case 1/(2x-1) since that number is common to both sides:
1/(2x-1) * (3x + 1)(2x -1) = (2x - 1) (4x + 3) * 1/(2x -1)
This eliminates the (2x -1) from both sides:
3x + 1 = 4x + 3
Now subtract 3x from both sides:
-3x + 3x + 1 = 4x + 3 - 3x
Which results in:
1 = x + 3
Solve simply for x:
-3 + 1 = x + 3 - 3
-2 = x

Prove it's right by substituting -2 for x

(3x + 1)(2x -1) = (2x - 1) (4x + 3)
(3 * -2 + 1)(2 * -2 -1) = (2 * -2 - 1) (4 * -2 + 3)
(-6 + 1)(-4 -1) = (-4 - 1)(-8 + 3)
(-5)(-5) = (-5)(-5)
-25 = -25
TRUE!

Answer 3

Divide both sides by (2x-1)

(3x+1)(2x-1) ---- ---- (2x-1)(4x+3)
___________ = ____________

(2x-1) ----- ----- ----- (2x-1)


You can then cancel out (2x-1) on both sides

This leaves 3x+1 = 4x+3

Minus 3 from both sides (you MUST always do the same thing to both sides of the equation)

Leaving 3x-2 = 4x

It is now possible to take away 3x from both sides.

This leaves -2 = x
More commonly written as x = -2

Answer 4

errr.. im not sure if this is rite cos i havent done quadratics for years, but here what i came up with:

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

first i think you multiply out the brackets:
6x + 1 - x +1 = 8x + 3 - 4x + 6

then simplify:
5x + 2 = 7x + 9

take 7x over the other side:
7x - 5x + 2 = 9

So,

2x + 2 = 9

hope that helps!

xxx

Answer 5

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

divide both sides by (2x-1)

3x+1=4x+3

take the x's to one side and the numbers to the other side

3x-4x=3-1
-x=2
x=-2

Answer 6

first multiple out each side

then put all the terms on one side

and take it from there

6x^2 + 6X + 1 = 8 x^2 + 2x - 3
-2x^2 + 3x + 4 = 0
and solve as a quadratic
(-b +- sqrt 4ac ) / 2a type of thing

you have to check if I made a mistake

Answer 7

Can't you divide both sides by (2x-1) leaving 3x+1=4x+3?
Then you can substract 4x from both sides leaving -x+1=3
Then you can substract 1 from both sides leaving -x=2
Therefore x= -2 ?

Answer 8

1) 12x+16=14x+21-9 12x-14x=21-9-16 2x=-4 x= -4/2 x=-2

Answer 9

Glen's correct, x = -2