Question

# Solve for y: (7y+3)/2=((8y+1)/6)+23 Simplify your answer as much as possible.

Probability and combinatorics
Solve for y: $$\displaystyle\frac{{{7}{y}+{3}}}{{2}}={\left(\frac{{{8}{y}+{1}}}{{6}}\right)}+{23}$$
Simplify your answer as much as possible.

2021-05-12
We are given: $$\displaystyle\frac{{{7}{y}+{3}}}{{2}}={\left(\frac{{{8}{y}+{1}}}{{6}}\right)}+{23}$$
Multiply both sides by the LCD which is 6: $$\displaystyle\frac{{{7}{y}+{3}}}{{2}}{\left({6}\right)}={\left({\left(\frac{{{8}{y}+{1}}}{{6}}\right)}+{23}\right)}{\left({6}\right)}$$
21y+9=(8y+1)+138
21y+9=8y+139
Subtract 9 from both sides: 21y=8y+130
Subtract 8y from both sides: 13y=130
Divie both sides by 13: y=10