To solve the equation, we first need to isolate x.
Step 1: Simplify both sides of the equation2 1/3 : (x-1 1/6) = 1 5/97/3 : (x-7/6) = 14/9
Step 2: Multiply both sides by the reciprocal of 7/3[(7/3) (3/7)] : (x-7/6) = (14/9) (3/7)1 : (x-7/6) = 42/631 : (x-7/6) = 2/3
Step 3: Multiply both sides by the reciprocal of the fraction on the left side1 (6/1) : (x-7/6) (6/1) = 2/3 * 6/16 : 6(x-7) = 12/3
Step 4: Simplify the equation6 : 6x - 42 = 46x - 42 = 4
Step 5: Add 42 to both sides6x - 42 + 42 = 4 + 426x = 46
Step 6: Divide by 6x = 46/6x = 23/3
Therefore, x = 23/3 or 7 2/3.
To solve the equation, we first need to isolate x.
Step 1: Simplify both sides of the equation
2 1/3 : (x-1 1/6) = 1 5/9
7/3 : (x-7/6) = 14/9
Step 2: Multiply both sides by the reciprocal of 7/3
[(7/3) (3/7)] : (x-7/6) = (14/9) (3/7)
1 : (x-7/6) = 42/63
1 : (x-7/6) = 2/3
Step 3: Multiply both sides by the reciprocal of the fraction on the left side
1 (6/1) : (x-7/6) (6/1) = 2/3 * 6/1
6 : 6(x-7) = 12/3
Step 4: Simplify the equation
6 : 6x - 42 = 4
6x - 42 = 4
Step 5: Add 42 to both sides
6x - 42 + 42 = 4 + 42
6x = 46
Step 6: Divide by 6
x = 46/6
x = 23/3
Therefore, x = 23/3 or 7 2/3.