Solve y−6x+1=34 for y.

Step 1
An equation consists an equal symbol between two algebraic expressions that have the same value. The common algebraic equations in math consist of one or more variables. The solution of variable must satisfy the equation.
Step 2
The given equation is $\frac{(y-6)}{(x+1)}=\frac{3}{4}$. Solve for y using the given equation as follows;
$\frac{(y-6)}{(x+1)}=\frac{3}{4}$
${\displaystyle \frac{(y-6)}{(x+1)}=\frac{3}{4}}$...Rewrite.
4(y-6)=3(x+1)...Apply cross fraction multiply if ${\displaystyle \frac{a}{b}=\frac{c}{d}}$ then a*d=c*b
4y-24=3x+3
4y−24+24=3x+3+24...Add 24 on both sides.
4y=3x+27
${\displaystyle \frac{4y}{4}=\frac{3x+27}{4}}$...Divide both sides by 4.
${\displaystyle t=\frac{3}{4}x+\frac{27}{4}}$
$=\frac{3x}{4}+\frac{27}{4}$
Hence, the solution of y for given equation $\frac{y-6}{(x+1)}=\frac{3}{4}$ is $y=\frac{3x}{4}+\frac{27}{4}$.