Determine whether the given problem is an equation or an expression. If it is an

Khadija Wells 2021-09-30 Answered

Determine whether the given problem is an equation or an expression. If it is an equation, then solve. If it is an expression, then simplify. \(\displaystyle\frac{{{5}{n}}}{{6}}-\frac{n}{{8}}=-\frac{17}{{12}}\)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

cyhuddwyr9
Answered 2021-10-01 Author has 11209 answers
Step 1
We have to determine whether the given problem is equation or expression. If it is an equation then we have to solve and if it is expression then simplify where problem is:
\(\displaystyle{\frac{{{5}{n}}}{{{6}}}}-{\frac{{{n}}}{{{8}}}}=-{\frac{{{17}}}{{{12}}}}\)
We know that
Expression can be any numbers, variables or combination of number and variable connected through mathematical operations.
Example:
\(\displaystyle{3},{x}^{{{2}}},{5}+{17}{x}\), ...
Equation is connected through equal sign where each side should be any expression.
Example:
\(\displaystyle{x}={y},{x}^{{{2}}}+{3}={0},{x}^{{{2}}}+{2}{x}={7}\), ...
The given problem have two expressions connected through equal sign.
Hence, it is an equation.
Step 2
Now solving the equation by taking LCM of the denominator in LHS side, we get
\(\displaystyle{\frac{{{5}{n}}}{{{6}}}}-{\frac{{{n}}}{{{8}}}}=-{\frac{{{17}}}{{{12}}}}\)
\(\displaystyle{\frac{{{5}{n}\times{4}-{3}\times{n}}}{{{24}}}}=-{\frac{{{17}}}{{{12}}}}\)
\(\displaystyle{\frac{{{20}{n}-{3}{n}}}{{{24}}}}=-{\frac{{-{17}}}{{{12}}}}\)
\(\displaystyle{\frac{{{17}{n}}}{{{24}}}}=-{\frac{{{17}}}{{{12}}}}\)
\(\displaystyle{12}\times{17}{n}=-{17}\times{24}\)
\(\displaystyle{n}={\frac{{-{17}\times{24}}}{{{12}\times{17}}}}\)
=-2
Hence, solution of the equation is n=−2.
Have a similar question?
Ask An Expert
40
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-09-23

Determine whether the given problem is an equation or an expression. If it is an equation, then solve. If it is an expression, then simplify. \(x + \frac{(3x - 1)}{9} - 4 = \frac{3x + 1}{3}\)

asked 2021-09-22

Determine whether the given problem is an equation or an expression. If it is an equation, then solve. If it is an expression, then simplify. \(n - \frac{3n + 1}{6} - 1 = \frac{2n + 4}{12}\)

asked 2021-10-01

Determine whether the given problem is an equation or an expression. If it is an equation, then solve. If it is an expression, then simplify. \(\displaystyle\frac{{{2}{x}+{7}}}{{8}}+{x}-{2}=\frac{{{x}-{1}}}{{2}}\)

asked 2021-09-24
Determine whether the given problem is an equation or an expression. If it is an equation, then solve. If it is an expression, then simplify. (4x - 1)/10 - (5x + 2)/4 = -3
asked 2021-09-18
Determine whether the given problem is an equation or an expression. If it is an equation, then solve. If it is an expression, then simplify. 1/2 (2x - 1) - 1/3 (5x + 2) = 3
asked 2021-09-28

Determine whether the given problem is an equation or an expression. If it is an equation, then solve. If it is an expression, then simplify. \(3x-1 + \frac{2}{7}(7x-2) = -\frac{11}{7}\)

asked 2021-09-24
Determine whether the given problem is an equation or an expression. If it is an equation, then solve. If it is an expression, then simplify. y/3 + (y - 5)/10 = (4y + 3)/5
...