(4x-3)-4x%5E2%2B5%2F4x%2B1%3D2.jpeg "(x+1)(4x-3)-4x^2+5/4x+1=2")
Solving the Equation: (x+1)(4x-3)-4x^2+5/4x+1=2
This article will guide you through the steps of solving the given equation: (x+1)(4x-3)-4x^2+5/4x+1=2.
Simplifying the Equation
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Expand the product: Start by expanding the product (x+1)(4x-3) using the distributive property (or FOIL method): (x+1)(4x-3) = 4x² - 3x + 4x - 3 = 4x² + x - 3
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Rewrite the equation: Now, substitute this expansion back into the original equation: 4x² + x - 3 - 4x² + 5/4x + 1 = 2
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Combine like terms: Notice that the terms 4x² and -4x² cancel each other out. Combine the remaining terms: x + 5/4x - 2 = 2
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Simplify the fraction: To combine the 'x' terms, we need a common denominator. Multiply the first 'x' term by 4/4: (4/4)x + 5/4x - 2 = 2 9/4x - 2 = 2
Solving for 'x'
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Isolate the 'x' term: Add 2 to both sides of the equation: 9/4x = 4
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Multiply both sides by the reciprocal: Multiply both sides by 4/9, the reciprocal of 9/4, to isolate 'x': (4/9) * (9/4)x = 4 * (4/9) x = 16/9
Solution
Therefore, the solution to the equation (x+1)(4x-3)-4x^2+5/4x+1=2 is x = 16/9.