# To calculate: The equation 3y+2\left[5\left(y-4\right)-2\right]=5y+

To calculate: The equation $$\displaystyle{3}{y}+{2}{\left[{5}{\left({y}-{4}\right)}-{2}\right]}={5}{y}+{6}{\left({7}+{y}\right)}-{3}$$

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Fachur
Calculation:
Consider the given equation, $$\displaystyle{3}{y}+{2}{\left[{5}{\left({y}-{4}\right)}-{2}\right]}={5}{y}+{6}{\left({7}+{y}\right)}-{3}$$
Now, apply the distributive property:
$$\displaystyle{3}{y}+{2}{\left[{5}{\left({y}-{4}\right)}-{2}\right]}={5}{y}+{6}{\left({7}+{9}\right)}-{3}$$
$$\displaystyle{3}{y}+{2}{\left[{5}{y}—{20}-{2}\right]}={5}{y}+{42}+{6}{y}—{3}$$
$$\displaystyle{3}{y}+{10}{y}—{44}={5}{y}+{42}+{6}{y}—{3}$$
Combine the like terms:
$$\displaystyle{3}{y}+{10}{y}—{44}={5}{y}+{42}+{6}{y}—{3}$$
$$\displaystyle{13}{y}-{44}={11}{y}+{39}$$
Now, subtract I ly from both sides:
$$\displaystyle{13}{y}-{44}={11}{y}+{39}$$
$$\displaystyle{13}{y}—{44}—{11}{y}={11}{y}+{39}+{11}{y}$$
Combine the like terms:
$$\displaystyle{13}{y}—{44}—{11}{y}={11}{y}+{39}+{11}{y}$$
$$\displaystyle{2}{y}-{44}={39}$$
$$\displaystyle{2}{y}-{44}+{44}={39}+{44}$$
Combine the like terms:
$$\displaystyle{2}{y}={83}$$
Divide both sides by 2:
$$\displaystyle{y}={\frac{{{83}}}{{{2}}}}$$
Now, check the solution by put the value of y = © in the equation
$$\displaystyle{3}{y}+{2}{\left[{5}{\left({y}-{4}\right)}—{2}\right]}={5}{y}+{6}{\left({7}+{9}\right)}-{3}$$.
$$\displaystyle{3}{y}+{2}{\left[{5}{\left({y}-{4}\right)}-{2}\right]}={5}{y}+{6}{\left({7}+{y}\right)}-{3}$$
$$\displaystyle{3}{\left({\frac{{{83}}}{{{2}}}}\right)}+{2}{\left[{5}{\left({\frac{{{83}}}{{{2}}}}-{4}\right)}-{2}\right]}{\overset{{?}}{{=}}}{5}{\left({\frac{{{83}}}{{{2}}}}\right)}+{6}{\left({7}+{\frac{{{83}}}{{{2}}}}\right)}-{3}$$
$$\displaystyle{\left({\frac{{{249}}}{{{2}}}}\right)}+{2}{\left[{\left({\frac{{{415}}}{{{2}}}}-{20}\right)}-{2}\right]}{\overset{{?}}{{=}}}{\left({\frac{{{415}}}{{{2}}}}\right)}+{\left({42}+{\frac{{{498}}}{{{2}}}}\right)}-{3}$$
$$\displaystyle{\left({\frac{{{249}}}{{{2}}}}\right)}+{\left[{\frac{{{830}}}{{{2}}}}-{40}-{4}\right]}{\overset{{?}}{{=}}}{\left({\frac{{{415}}}{{{2}}}}\right)}+{42}+{\frac{{{498}}}{{{2}}}}-{3}$$
On further solution:
$$\displaystyle{\frac{{{249}}}{{{2}}}}+{\frac{{{830}}}{{{2}}}}-{44}{\overset{{?}}{{=}}}{\frac{{{415}}}{{{2}}}}+{\frac{{{498}}}{{{2}}}}+{39}$$
$$\displaystyle{\frac{{{249}+{830}-{88}}}{{{2}}}}{\overset{{?}}{{=}}}{\frac{{{415}+{498}+{78}}}{{{2}}}}$$
$$\displaystyle{\frac{{{991}}}{{{2}}}}{\overset{{?}}{{=}}}{\frac{{{991}}}{{{2}}}}$$
Hence, the solution set is $$\displaystyle{y}={\frac{{{83}}}{{{2}}}}$$.