### x-1/6=1/6

This deals with adding, subtracting and finding the least common multiple.

## Step by Step Solution

### Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : x-1/6-(1/6)=0

## Step by step solution :

## Step 1 :

1 Simplify — 6Equation at the end of step 1 : 1 1 (x – —) – — = 0 6 6

## Step 2 :

1 Simplify — 6Equation at the end of step 2 : 1 1 (x – —) – — = 0 6 6

## Step 3 :

Rewriting the whole as an Equivalent Fraction :3.1Subtracting a fraction from a whole Rewrite the whole as a fraction using 6 as the denominator :

x x • 6 x = — = ————— 1 6 Equivalent fraction : The fraction thus generated looks different but has the same value as the whole Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :3.2 Adding up the two equivalent fractions Add the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • 6 – (1) 6x – 1 ——————————— = —————— 6 6 Equation at the end of step 3 : (6x – 1) 1 ———————— – — = 0 6 6

## Step 4 :

Adding fractions which have a common denominator :4.1 Adding fractions which have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(6x-1) – (1) 6x – 2 ———————————— = —————— 6 6

## Step 5 :

Pulling out like terms :5.1 Pull out like factors:6x – 2=2•(3x – 1)

Equation at the end of step 5 : 2 • (3x – 1) ———————————— = 0 6

## Step 6 :

When a fraction equals zero :6.1 When a fraction equals zero …Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.Here”s how:

2•(3x-1) ———————— • 6 = 0 • 6 6 Now, on the left hand side, the 6 cancels out the denominator, while, on the right hand side, zero times anything is still zero.The equation now takes the shape:2 • (3x-1)=0

Equations which are never true:6.2Solve:2=0This equation has no solution. A a non-zero constant never equals zero.

Solving a Single Variable Equation:6.3Solve:3x-1 = 0Add 1 to both sides of the equation:3x = 1 Divide both sides of the equation by 3:x = 1/3 = 0.333