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If m+1=(5(m-1))/(3), then (1)/(m)=...

If `m+1=(5(m-1))/(3)`, then `(1)/(m)=`

A

`(1)/(4)`

B

`(3)/(8)`

C

`2`

D

`(8)/(3)`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the equation \( m + 1 = \frac{5(m - 1)}{3} \), we will follow these steps: ### Step 1: Eliminate the fraction Multiply both sides of the equation by 3 to eliminate the fraction: \[ 3(m + 1) = 5(m - 1) \] ### Step 2: Distribute on both sides Distribute the 3 on the left side and the 5 on the right side: \[ 3m + 3 = 5m - 5 \] ### Step 3: Rearrange the equation Now, we will move all terms involving \( m \) to one side and constant terms to the other side. Subtract \( 3m \) from both sides: \[ 3 = 5m - 3m - 5 \] This simplifies to: \[ 3 = 2m - 5 \] ### Step 4: Isolate \( m \) Next, add 5 to both sides to isolate the term with \( m \): \[ 3 + 5 = 2m \] This simplifies to: \[ 8 = 2m \] ### Step 5: Solve for \( m \) Now, divide both sides by 2 to find \( m \): \[ m = \frac{8}{2} = 4 \] ### Step 6: Find \( \frac{1}{m} \) Now that we have \( m = 4 \), we can find \( \frac{1}{m} \): \[ \frac{1}{m} = \frac{1}{4} \] Thus, the value of \( \frac{1}{m} \) is \( \frac{1}{4} \). ### Final Answer The correct option is \( \frac{1}{4} \). ---
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