Intermediate Algebra (12th Edition)

$x=-1$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $\dfrac{3x-1}{5}+\dfrac{x+2}{2}=-\dfrac{3}{10} ,$ multiply both sides by the $LCD.$ Then use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ The $LCD$ of the denominators $\{ 5,2,10 \}$ is $10$ since it is the smallest number which can be divided by all the denominators. Multiplying both sides of the given equation by the $LCD= 10$ results to \begin{array}{l}\require{cancel} 2(3x-1)+5(x+2)=1(-3) .\end{array} Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 6x-2+5x+10=-3 .\end{array} Using the properties of equality to combine like terms, the equation above is equivalent to \begin{array}{l}\require{cancel} 6x+5x=-3+2-10 \\\\ 11x=-11 \\\\ x=-\dfrac{11}{11} \\\\ x=-1 .\end{array}