How do you solve #(3x-1)/3-(x-3)/15=(2x+3)/2#?

Question

Ethan Adkins · Accepted Answer

Separate the first section: #(3x - 1)/3 - (x-3)/15# Since 15 is a common multiple of 3 and 15, multiply the first fraction by 5 and the second by 1 to get the denominator (both bottom numbers) equal. #(5(3x - 1))/15 - (x-3)/15 # Now expand and subtract the two #(15x -5 )/15 - (x - 3)/15# #(15x - 5 - x + 3)/15 = (14x - 2)/15# Reintroduce it into the entire formula: #(14x - 2)/15 = (2x + 3)/2#  Since they both have a multiple of 30, multiply the first by two and the second by fifteen. #(2(14x - 2))/30 = (15(2x + 3))/30 # #(28x - 4)/30 = (30x + 45)/30# #28x -4 = 30x + 45#
#-2x = 49# #x = -24.5#

Genesis Allen · Answer

undefined To solve the equation (3x-1)/3-(x-3)/15=(2x+3)/2, we can start by finding a common denominator for the fractions. The common denominator is 30. Multiplying each term by 30 will eliminate the denominators. Simplifying the equation gives us 10(3x-1) - 2(x-3) = 15(2x+3). Expanding and simplifying further, we get 30x - 10 - 2x + 6 = 30x + 45. Combining like terms, we have 28x - 4 = 30x + 45. Moving the variables to one side and the constants to the other side, we get 2x - 30x = 45 + 4. Simplifying, we have -28x = 49. Dividing both sides by -28, we find x = -49/28, which simplifies to -1.75. Therefore, the solution to the equation is x = -1.75.