Problem 121 - Introductory Algebra for College Students

Question

Determine whether the given number is a solution of the equation. $$\frac{1}{5}(x+2)=\frac{1}{2}\left(x-\frac{1}{5}\right) ; \frac{5}{8}$$

Step-by-Step Solution

Answer

No, \(\frac{5}{8}\) is not a solution to the equation.

Step 1: Substitute the given number

Firstly, substitute the given number \(\frac{5}{8}\) into the variable ‘x’ in the equation. The equation becomes: \(\frac{1}{5}((\frac{5}{8})+2)=\frac{1}{2}((\frac{5}{8})-\frac{1}{5})\)

Step 2: Simplify the equation

Simplify the fractions inside the parentheses: \(\frac{1}{5}((\frac{21}{8}))=\frac{1}{2}((\frac{5}{8})-\frac{1}{5})\). Then solve the right hand side of the equation: \(\frac{1}{5}((\frac{21}{8}))=\frac{1}{2}*(\frac{1}{40})\). Simplifying the above equations, we get \(\frac{21}{40}=\frac{1}{80}\).

Step 3: Analyze the result

The results \(\frac{21}{40}\) and \(\frac{1}{80}\) do not equate, so the given number \(\frac{5}{8}\) is not a solution for the equation.