Solve for x:3 (x + 1/5) = 7/10
Put each term in x + 1/5 over the common denominator 5: x + 1/5 = (5 x)/5 + 1/5:3 (5 x)/5 + 1/5 = 7/10
(5 x)/5 + 1/5 = (5 x + 1)/5:3 (5 x + 1)/5 = 7/10
Multiply both sides of (3 (5 x + 1))/5 = 7/10 by 5/3:(5×3 (5 x + 1))/(3×5) = (5×7)/(3×10)
(5×7)/(3×10) = (5×7)/(3×10):(5×3 (5 x + 1))/(3×5) = (5×7)/(3×10)
(5×3 (5 x + 1))/(3×5) = (3×5)/(3×5)×(5 x + 1) = 5 x + 1:5 x + 1 = (5×7)/(3×10)
5/10 = 5/(5×2) = 1/2:5 x + 1 = 7/(3×2)
3×2 = 6:5 x + 1 = 7/6
Subtract 1 from both sides:5 x + (1 - 1) = 7/6 - 11 - 1 = 0:5 x = 7/6 - 1
Put 7/6 - 1 over the common denominator 6. 7/6 - 1 = 7/6 - (6)/6:5 x = 7/6 - (6)/6
7/6 - (6)/6 = (7 - 6)/6:5 x = (7 - 6)/6
7 - 6 = 1:5 x = 1/6
Divide both sides of 5 x = 1/6 by 5:(5 x)/5 = 1/(6×5)
5/5 = 1:x = 1/(6×5)
6×5 = 30:Answer: x = 1/30