2021
Mathematics
67ca00ce0c643c71d77dee1f
Solve the following equation: 2(2r−1) - 5/3 = 1(r+2)
A.
( -1, 5/2 )
B.
( 1, - 5/2 )
C.
( 5/2, 1 )
D.
(2,1)
Correct Answer: ( 1, - 5/2 )
Explanation
2/(2r−1) - 5/3 = 1/(r+2) 2/(2r−1) - 1(r+2) = 5/3 The L.C.M.: (2r - 1) (r + 2) (2(r+2)−1(2r−1))/((2r−1)(r+2)) = 5/3 (2r + 4 − 2r + 1)/((2r−1)(r+2)) = 5/3 cross multiply the solution 3 * 5 = (2r - 1) (r + 2) * 5 divide both sides 5 3 = 2r2 + 3r - 2 (when expanded) collect like terms 2r222 -2r + 5r - 5 = 0 [2r2 -2r] [+ 5r - 5] = 0 2r(r-1) + 5(r-1) = 0 (2r+5) (r-1) = 0 r = 1 or - 5/2
2/(2r−1) - 5/3 = 1/(r+2) 2/(2r−1) - 1(r+2) = 5/3 The L.C.M.: (2r - 1) (r + 2) (2(r+2)−1(2r−1))/((2r−1)(r+2)) = 5/3 (2r + 4 − 2r + 1)/((2r−1)(r+2)) = 5/3 cross multiply the solution 3 * 5 = (2r - 1) (r + 2) * 5 divide both sides 5 3 = 2r2 + 3r - 2 (when expanded) collect like terms 2r222 -2r + 5r - 5 = 0 [2r2 -2r] [+ 5r - 5] = 0 2r(r-1) + 5(r-1) = 0 (2r+5) (r-1) = 0 r = 1 or - 5/2THIS WEEK's
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