## Intermediate Algebra (12th Edition)

$x=\dfrac{7}{6}$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $2x-5+3x=4-(x+2) ,$ combine like terms. Then use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 2x-5+3x=4-1(x+2) \\\\ 2x-5+3x=4-1(x)-1(2) \\\\ 2x-5+3x=4-x-2 .\end{array} Using the properties of equality to combine like terms, the equation above is equivalent to \begin{array}{l}\require{cancel} 2x+3x+x=4-2+5 \\\\ 6x=7 \\\\ x=\dfrac{7}{6} .\end{array}