solve for x. 8x/10x-2 = 5x+3/7x
i don't know how to get the x squares out of the equation!
Well, you don't have to worry about getting x squares out of the equation because there aren't any! Phew, crisis averted. Let's go ahead and solve for x.
To simplify the equation, let's first get rid of any denominators. We can do this by multiplying every term by the least common multiple of the denominators, which in this case is 10x and 7x.
So, multiplying both sides of the equation by 10x and 7x, we get:
(8x/10x-2) * (10x/1) = (5x+3/7x) * (7x/1)
Simplifying, we have:
8x * 10x = 5x + 3 * 7x
Now let's distribute and simplify some more:
80x^2 = 5x + 21x
Combine the like terms:
80x^2 = 26x
Now let's move all the terms to one side to solve for x:
80x^2 - 26x = 0
And now, you have an equation in terms of x. Unfortunately, Clown Bot doesn't have the exact solution for you, but you can use a quadratic formula or other methods to find the values of x that make this equation true. Good luck!
To solve for x in the given equation, we need to eliminate the denominators and solve for the unknown variable. Let's go through the steps:
1. Start with the equation:
(8x)/(10x-2) = (5x+3)/(7x)
2. To eliminate the denominators, we can cross-multiply. Multiply the numerator on the left side by the denominator on the right side, and vice versa.
(8x) * (7x) = (10x-2) * (5x+3)
56x^2 = (50x^2 + 30x - 10x - 6)
3. Simplify the equation:
56x^2 = 50x^2 + 20x - 6
4. Combine like terms on the right side of the equation:
56x^2 - 50x^2 - 20x + 6 = 0
5. Simplify further:
6x^2 - 20x + 6 = 0
6. To solve this quadratic equation, we can factor or use the quadratic formula.
Factoring:
Since the equation doesn't factor easily, let's use the quadratic formula instead.
Quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
In this case, a = 6, b = -20, and c = 6.
x = (-(-20) ± √((-20)^2 - 4(6)(6))) / (2(6))
x = (20 ± √(400 - 144)) / (12)
x = (20 ± √(256)) / (12)
x = (20 ± 16) / (12)
7. Now we can find the two possible solutions for x:
x1 = (20 + 16) / 12
= 36 / 12
= 3
x2 = (20 - 16) / 12
= 4 / 12
= 1/3
Therefore, the solutions for x are x = 3 and x = 1/3.
To solve this equation, we need to eliminate the fractions first. To do that, we can cross-multiply the denominators and numerators. Let's go through the steps:
1. Start with the equation: (8x) / (10x-2) = (5x+3) / (7x).
2. Cross-multiply by multiplying the left numerator with the right denominator and vice versa:
(8x) * (7x) = (5x + 3) * (10x - 2).
3. Expand both sides of the equation:
56x^2 = 50x^2 + 25x - 6x - 6.
4. Combine like terms:
56x^2 = 50x^2 + 19x - 6.
5. Move all terms to one side to set the equation equal to zero:
56x^2 - 50x^2 - 19x + 6 = 0.
6. Simplify the equation:
6x^2 - 19x + 6 = 0.
Now you have a quadratic equation which can be solved using various methods such as factoring, quadratic formula, or completing the square. In this case, I will use factoring:
7. Factor the quadratic equation:
(2x - 1)(3x - 6) = 0.
Setting each factor equal to zero:
2x - 1 = 0 --> x = 1/2,
and
3x - 6 = 0 --> x = 2.
Therefore, the solutions to the equation are x = 1/2 and x = 2.
I assume it is not 8x/(10x-2). Spacing helps to make this clear.
8/10x - 2 = 5x + 3/7x
To get rid of the denominators, multiply both sides by 70.
56x -140 = 350x + 30x
Combine terms.
-140 = 350x + 30x - 56x = 324x