## Elementary Algebra

$x=-\dfrac{9}{40}$
Multiplying both sides of the equation by the least common multiple of the denominators, which is 40, and using the properties of equality, the value of the variable that satisfies the given equation, $x+\dfrac{5}{8}=\dfrac{2}{5} ,$ is \begin{array}{l}\require{cancel} 40\left( x+\dfrac{5}{8} \right)=\left( \dfrac{2}{5} \right)40 \\\\ 40(x)+5(5)=2(8) \\\\ 40x+25=16 \\\\ 40x=16-25 \\\\ 40x=-9 \\\\ x=-\dfrac{9}{40} .\end{array}