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# how do you solve 5/3 (1/2x – 5) = 3x + 15 ?

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- LukeLv 68 years agoFavorite Answer
given:

(5 / 3) (1 / (2x) - 5) = 3x + 15

multiply both sides by the reciprocal of (5 / 3) which is (3 / 5)

(3 / 5)(5 / 3) (1 / (2x) - 5) = (3 / 5)(3x + 15)

simplify

(1 / (2x) - 5) = (3 / 5)(3x + 15)

(1 / (2x) - 5) = (9 / 5)x + 9

multiply both sides by 10x to clear the fractions

(10x)(1 / (2x) - 5) = (10x)((9 / 5)x + 9)

simplify

5 - 50x = 18x^2 + 90x

rearranging gives us quadratic equation form

18x^2 + 140x - 5 = 0

quadratic coefficients are: a = 18 , b = 140 , c = -5

using the quadratic formula gives us:

x = (-35 / 9) + (1 / 18) sqrt(4990)

or

x = (-35 / 9) - (1 / 18) sqrt(4990)

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