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Algebra

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Given (14x+22)/(2x+18)=3x+1, compute the sum of all the possible values of x.

Aug 1, 2021

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(14x+22)/(2x+18)=3x+1       Multiply both sides of the equation by (2x+18)

14x +22 = (3x+1)(2x+18)     expand and simplify to

6x^2+42x-4 = 0     Now use Quadratic Formula       to find x values

a = 6    b = 42    c = -4    in the Quadratic Formula

$$x = {-42 \pm \sqrt{42^2-4(6)(-4)} \over 2(6)}$$

Aug 1, 2021