Answer :
GIVEN:
We are given the following equation;
[tex]16x+9=9y-2x[/tex]Required;
Solve the equation for y.
Step-by-step solution;
To solve, we simply collect like terms as follows;
[tex]\begin{gathered} Add\text{ }2x\text{ }to\text{ }both\text{ }sides: \\ 16x+2x+9=9y-2x+2x \end{gathered}[/tex]We now have;
[tex]18x+9=9y[/tex]Observe that -2x and +2x cancel out each other on the right hand side.
Next step, we divide both sides by 9, that is the coefficient of y.
[tex]\frac{18x+9}{9}=\frac{9y}{9}[/tex][tex]\frac{18x+9}{9}=y[/tex]Note that we can split up the left hand side. We do this by taking both numbers in the numerator and writing each as a fraction with 9 as the denominator. This is because 9 is the LCM of both fractions as it is expressed above.
We now have;
[tex]\frac{18x}{9}+\frac{9}{9}=y[/tex]Now we divide both fractions by any common factors;
[tex]2x+1=y[/tex]Therefore,
ANSWER:
[tex]y=2x+1[/tex]