Solving the Linear Equation 3y - 4 = 6v - 4

Solving Linear Equations

Equation to Solve

• The equation given is:
  $3y - 4 = 6v - 4$

Steps to Solve the Equation

1. Isolate Terms Involving Variables

   • To solve for either $y$ or $v$, first, we notice that the equation can be simplified by eliminating the $-4$ on both sides:
     • Add $4$ to both sides of the equation:
       $3y - 4 + 4 = 6v - 4 + 4$
       This simplifies to:
       $3y = 6v$

2. Simplify the Equation Further

   • Now, we can see that the equation is linear in terms of $y$ and $v$.
   • We can solve for $y$ in terms of $v$:
     • Divide both sides by $3$:
       $y = \frac{6}{3}v$
       Which simplifies to:
       $y = 2v$

Solution Set

• The solution set for the equation is expressed as:
  $y = 2v$
  This indicates that for every value of $v$, there is a corresponding value of $y$ that is twice that value.

Conclusion

• The final relationship between $y$ and $v$ is represented by the equation: $y = 2v$. The solution captures all pairs $(y, v)$ such that $y$ is always twice the corresponding value of $v$.