Question

Solve for v,7+ 2/v-6 = 3v/v-6I

Answer 1

Given the question in the question tab, the following are the solution steps to answer the question.

STEP 1: Write the given question.

`7+(2)/(v-6)=(3v)/(v-6)`

STEP 2: Simplify the expression.

Multiply both sides by v-6

`\begin{gathered} 7\mleft(v-6\mright)+(2)/(v-6)\mleft(v-6\mright)=(3v)/(v-6)\mleft(v-6\mright) \\ \text{Simplify as (v-6) cancels out each other} \\ 7\mleft(v-6\mright)+2=3v \end{gathered}`

STEP 3: Expand the Left Hand side

`\begin{gathered} 7(v-6)+2\Rightarrow7v-42+2\Rightarrow7v-40 \\ \text{Rewrite the equation;} \\ 7v-40=3v \end{gathered}`

STEP 4: Add 40 to both sides

`\begin{gathered} 7v-40+40=3v+40 \\ \text{Simplify;} \\ 7v=3v+40 \end{gathered}`

STEP 5: Subtract 3v from both sides

`\begin{gathered} 7v-3v=3v+40-3v \\ 4v=40 \end{gathered}`

STEP 6: Divide both sides by 4

`\begin{gathered} (4v)/(4)=(40)/(4) \\ v=10 \end{gathered}`

Hence, the value of v is 10