(8w+5)/(10w-7) = (4w-3)/(5w+7)
How would I solve this?
Do you know how to cross multiply and simplify the equation to a quadratic?
cross-multiply
(8w+5)(5w+7) = (4w-3)(10w-7)
40w^2 + 81w + 35 = 40w^2 -58w + 21
139w = -14
w = -14/139
To solve this equation, you can follow these steps:
Step 1: Cross-multiply
Multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa. This will eliminate the fractions and give you a new equation to work with.
(8w + 5)(5w + 7) = (10w - 7)(4w - 3)
Step 2: Expand and simplify
Expand both sides of the equation using the distributive property.
40w^2 + 56w + 25w + 35 = 40w^2 - 30w - 28w + 21
Combine like terms to simplify:
40w^2 + 81w + 35 = 40w^2 - 58w + 21
Step 3: Collect like terms
Rearrange the equation by moving all the terms to one side, which will result in a quadratic equation:
40w^2 - 40w^2 + 81w + 58w - 35 - 21 = 0
Combine like terms:
139w - 56 = 0
Step 4: Solve for w
Isolate the variable on one side of the equation by moving the constant term to the other side:
139w = 56
Finally, divide both sides of the equation by the coefficient of w (139) to solve for w:
w = 56 / 139
So the solution to the equation is w = 0.403, rounded to three decimal places.