4x+3/2x-1-2 = 6x+2/2x-1
(4x+3)(-2) = (6x+2)
-8x-6 = 6x+2
-14x-6 = 2
-14x = 8
x = 4/-7
i not think i did this right.
do you mean
[ (4x+3)/(2x-1) ] - 2 = (6x+2)/(2x-1)
??????
If so please use parentheses so I can tell numerator from denominator.
If my guess is correct:
(4x+3) -2 (2x-1) = 6x+2
4x + 3 -4x + 2 = 6 x + 2
3 = 6 x
x = 1/2
sorry yes you are right but don't all 2x-1's cancel?
i think it supposed to be this
(4x+3)(-2) = (6x+2)
[ (4x+3)/(2x-1) ] - 2 = (6x+2)/(2x-1)
Multiply everything, all terms both sides including -2, by (2x-1)
[(4x+3)/(2x-1)](2x-1)-2(2x-1) = [(6x+2)/(2x-1) ] (2x-1)
You have to multiply that -2 by (2x-1) so the (2x-1) does not go away from the numerator when you clear it from the denominators.
so
(4x+3) -2 (2x-1) = 6x + 2
Perhaps your original line should read
[(4x+3)/(2x-1)](-2) = (6x+2)/(2x-1)
if so then
-2(4x+3) = 6x+2
-8x - 6 = 6x + 2
-14 x = 8
x = -4/7
and your answer would be right
thank you but in back of book it say no solution so i very confused.
If my solution of x = 1/2 is correct (and I think it is'
Then indeed the answer is NO SOLUTION
because
2x-1 = 0 if x = 1/2
division by 0
I did not notice that, should have.
thank you so much i not notice that either. thanks :)
To solve the equation 4x + (3/2x - 1) - 2 = 6x + (2/2x - 1), let's break it down step by step.
First, we need to simplify the expression inside each parentheses to make it easier to work with.
In the left parentheses, we have (3/2x - 1). To simplify this, we need a common denominator for the fractions. The denominator of the first fraction is 2x, so we'll multiply the second term (-1) by 2x to get -2x.
The expression now becomes (3 - 2x)/2x - 1.
Similarly, in the right parentheses, we have (2/2x - 1). Again, we need a common denominator, which is 2x. The expression becomes (2 - 2x)/2x - 1.
Now, let's rewrite the equation with the simplified expressions:
4x + (3 - 2x)/2x - 1 - 2 = 6x + (2 - 2x)/2x - 1.
Next, we need to clear the denominators in the equation. To do this, we'll multiply each term by the common denominator, which is 2x.
2x * 4x + (3 - 2x) - 2x * 1 - 2 * 2x = 2x * 6x + (2 - 2x) - 2x * 1 - 1 * 2x.
This simplifies to:
8x^2 + 3 - 2x - 2x - 4x = 12x^2 + 2 - 2x - 2x - 2x.
Combine like terms:
8x^2 - 8x + 3 = 12x^2 - 6x.
Now, let's move all the terms to one side of the equation to solve for x. Subtracting the right side from both sides:
8x^2 - 8x + 3 - (12x^2 - 6x) = 0.
This simplifies to:
8x^2 - 12x^2 - 8x + 6x + 3 = 0.
Combining like terms:
-4x^2 -2x + 3 = 0.
Now, you can solve this quadratic equation. There are different methods like factoring, completing the square, or using the quadratic formula. Let's solve it using the quadratic formula:
x = (-(-2) ± sqrt((-2)^2 - 4(-4)(3))) / (2(-4)).
This simplifies to:
x = (2 ± sqrt(4 + 48)) / (-8).
x = (2 ± sqrt(52)) / (-8).
Further simplifying:
x = (2 ± sqrt(4 * 13)) / (-8).
x = (2 ± 2 sqrt(13)) / (-8).
Simplifying the fraction and reducing:
x = (1 ± sqrt(13)) / (-4).
Therefore, the solutions to the equation are x = (1 + sqrt(13))/(-4) and x = (1 - sqrt(13))/(-4).