Solve for x: (2 (1-2 x))/5-1/5 = 15 (2 (1-2 x))/5-1/5 = (2 (1-2 x)-1)/5: (2 (1-2 x)-1)/5 = 15 2 (1-2 x) = 2-4 x: (2-4 x-1)/5 = 15 Add like terms. 2-1 = 1: (1-4 x)/5 = 15 Multiply both sides of (1-4 x)/5 = 15 by 5: (5 (1-4 x))/5 = 5×15 (5 (1-4 x))/5 = 5/5×(1-4 x) = 1-4 x: 1-4 x = 5×15 5×15 = 75: 1-4 x = 75 Subtract 1 from both sides: (1-1)-4 x = 75-1 1-1 = 0: -4 x = 75-1 75-1 = 74: -4 x = 74 Divide both sides of -4 x = 74 by -4: (-4 x)/(-4) = 74/(-4) (-4)/(-4) = 1: x = 74/(-4) The gcd of 74 and -4 is 2, so 74/(-4) = (2×37)/(2 (-2)) = 2/2×37/(-2) = 37/(-2): x = 37/(-2) Multiply numerator and denominator of 37/(-2) by -1: Answer: | | x = (-37)/2
Solve for x: (2 (1-2 x))/5-1/5 = 15 (2 (1-2 x))/5-1/5 = (2 (1-2 x)-1)/5: (2 (1-2 x)-1)/5 = 15 2 (1-2 x) = 2-4 x: (2-4 x-1)/5 = 15 Add like terms. 2-1 = 1: (1-4 x)/5 = 15 Multiply both sides of (1-4 x)/5 = 15 by 5: (5 (1-4 x))/5 = 5×15 (5 (1-4 x))/5 = 5/5×(1-4 x) = 1-4 x: 1-4 x = 5×15 5×15 = 75: 1-4 x = 75 Subtract 1 from both sides: (1-1)-4 x = 75-1 1-1 = 0: -4 x = 75-1 75-1 = 74: -4 x = 74 Divide both sides of -4 x = 74 by -4: (-4 x)/(-4) = 74/(-4) (-4)/(-4) = 1: x = 74/(-4) The gcd of 74 and -4 is 2, so 74/(-4) = (2×37)/(2 (-2)) = 2/2×37/(-2) = 37/(-2): x = 37/(-2) Multiply numerator and denominator of 37/(-2) by -1: Answer: | | x = (-37)/2
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