## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$x=5$
$\bf{\text{Solution Outline:}}$ Use the Distributive Property and the properties of equality to find the solution to the given equation, $3(x-2)=14-x .$ $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the equation above is equivalent to \begin{array}{l}\require{cancel} 3(x-2)=14-x \\\\ 3(x)+3(-2)=14-x \\\\ 3x-6=14-x .\end{array} Using the properties of equality, the equation above is equivalent to \begin{array}{l}\require{cancel} 3x-6=14-x \\\\ 3x+x=14+6 \\\\ 4x=20 \\\\ x=\dfrac{20}{4} \\\\ x=5 .\end{array}