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

leviattan0pi 2021-11-20 Answered
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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Expert Answer

Fachur
Answered 2021-11-21 Author has 8795 answers
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:
\(\displaystyle{13}{y}—{44}—{11}{y}={11}{y}+{39}+{11}{y}\)
\(\displaystyle{2}{y}-{44}={39}\)
Add 44 to both sides:
\(\displaystyle{2}{y}-{44}+{44}={39}+{44}\)
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 \(\displaystyle{y}={\frac{{{83}}}{{{2}}}}\).
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