Anthony A. answered • 10/14/19
Hi, I'm Anthony a data analyst in the healthcare field.
First: You want to isolate the x variables and the constants (move the x's to one side and the constants on the other)
subtract x/3 from both sides (x/3 - x/3) + 1/5 = (x/2 - 1/4 + 3x/2) - x/3 <=> 1/5 = x/2 - 1/4 + 3x/2 -x/3
add 1/4 to both sides 1/5 + 1/4 = x/2 - 1/4 + 1/4 + 3x/2 - x/3 <=> 1/5 + 1/4 = x/2 + 3x/2 - x/3
Second: You combine the fractions on the left (1/5 + 1/4) by getting like-denominators
(1/5 = 4/20, 1/4 = 5/20) => 4/20 + 5/20 = 9/20
Third: You combine the fractions on the right (x/2 + 3x/2 - x/3) by getting like-denominators
(x/2 = 3x/6, 3x/2 = 9x/6, -x/3 = -2x/6) => (3x/6 + 9x/6 - 2x/6) = 10x/6 = (10/6)x
Fourth: Multiply by the reciprocal of the fraction to both sides to get x by itself (6/10)(9/20) = (6/10)(10/6)x
(6/10)(9/20) = x
Fifth and Final: Simplify the fraction on the left (6/10)(9/20) = (6 * 9)/(10 * 20) = 54/200 = 27/100
therefore 27/100 = x
