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How do you solve #7 - 7x = (4x + 9)(x - 1)#?

Answer 1

x = -4 , 1

7 - 7x = (4x + 9) (x - 1) or, 7 - 7x = 4x((x-1) + 9(x-1) or, 7 - 7x = 4#x^2# -4x +9x -9 or, 0 = 4#x^2#+5x +7x-7-9 or, 4#x^2#+12x-16 = 0 0r, 4#x^2#+(16-4)x-16 = 0 or, 4#x^2#+16x -4x-16 = 0 or, 4x(x+4) - 4(x+4) = 0 or, (x+4) (4x -4) = 0 Either (x+4) = 0 x = -4 Or, (4x-4) = 0 or, 4x =4 or, x = #4/4# or, x = 1 Hence x = -4 , 1

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Answer 2

Eva Adamson

To solve the equation 7 - 7x = (4x + 9)(x - 1), follow these steps:

Expand the right side of the equation: (4x + 9)(x - 1) = 4x^2 - 4x + 9x - 9 = 4x^2 + 5x - 9.
Rewrite the equation with the expanded form of the right side: 7 - 7x = 4x^2 + 5x - 9.
Rearrange the terms to set the equation to zero: 4x^2 + 5x - 7x - 9 - 7 = 0.
Combine like terms: 4x^2 - 2x - 16 = 0.
Now, you can either factor or use the quadratic formula to solve for x.

If you choose to factor, you'd find that the equation factors to (2x - 8)(2x + 2) = 0.

Setting each factor equal to zero gives you the solutions: 2x - 8 = 0 => x = 4, 2x + 2 = 0 => x = -1.

Therefore, the solutions to the equation are x = 4 and x = -1.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.