Question

Find x:

`(x-4)/(5)` -
`(x+1)/(6)` =
`(1)/(6)`

Answer 1

34

Explanation:

Multiplying both sides by 30,

`6(x-4)-5(x+1)=5 \\ \\ 6x-24-5x-5=5 \\ x-29=5 \\ \\ x=34`

Answer 2

The value of x is 34.

Step-by-step explanation:

QUESTION :

Find x:

`\sf{\implies{(x - 4)/(5) - (x+1)/(6) = (1)/(6)}}`

`\begin{gathered} \end{gathered}`

CONCEPT :

Here, we will use the below following steps to find a solution using the transposition method:

• Step 1 :- we will Identify the variables and constants in the given simple equation.
• Step 2 :- then we Simplify the equation in LHS and RHS.
• Step 3 :- Transpose or shift the term on the other side to solve the equation further simplest.
• Step 4 :- Simplify the equation using arithmetic operation as required that is mentioned in rule 1 or rule 2 of linear equations.
• Step 5 :- Then the result will be the solution for the given linear equation.

`\begin{gathered} \end{gathered}`

SOLUTION :

`\sf{\implies{(x - 4)/(5) - (x+1)/(6) = (1)/(6)}}`

Taking LCM of both denominators.

`\sf{\implies{ (6(x - 4) - 5(x + 1))/(30) = (1)/(6)}}`

`\sf{\implies{ (6x - 24 - 5x - 5)/(30) = (1)/(6)}}`

`\sf{\implies{ (x - 29)/(30) = (1)/(6)}}`

`\sf{\implies{ x - 29 = (1)/(6) * 30}}`

`\sf{\implies{ x - 29 = 5}}`

`\sf{\implies{ x = 5 + 24}}`

`\sf{\implies{\underline{\underline{ x =34}}}}`

Hence, the value of x is 34.

`\begin{gathered} \end{gathered}`

Verification :

`\sf{\implies{(x - 4)/(5) - (x+1)/(6) = (1)/(6)}}`

Substituting the value of x in the equation :

`\sf{\implies{(34 - 4)/(5) - (34+1)/(6) = (1)/(6)}}`

`\sf{\implies{(30)/(5) - (35)/(6) = (1)/(6)}}`

`\sf{\implies{((30 * 6) - (35 * 5))/(30) = (1)/(6)}}`

`\sf{\implies{((180) - (175))/(30) = (1)/(6)}}`

`\sf{\implies{(5)/(30) = (1)/(6)}}`

`\sf{\implies{\cancel{(5)/(30)} = (1)/(6)}}`

`\sf{\implies{(1)/(6) = (1)/(6)}}`

`\sf{\implies{\underline{\underline{LHS = RHS}}}}`

Hence verified!

————————————————