one sixth of the sum of twice a number and 1 is the same as one quarter of the difference between three times the number and 1. find the number.

Answer 1

Just translate that confusing English into Math

"one sixth of the sum of twice a number and 1" ----> (2x + 1)/6
"is the same as " ----> =
"one quarter of the difference between three times the number and 1"
---- (3x - 1)/4
(3x - 1)/4 = (2x + 1)/6
times 12 to clear fractions
3(3x-1) = 2(2x + 1)
9x - 3 = 4x + 2
5x = 5
x = 1

The number is 1

Check: one sixth of the sum of twice a number and 1 = (1/6)(2 + 1) = 1/2
one quarter of the difference between three times the number and 1 = (1/4)(3-1) = 1/2
they are the same, my answer is correct